Catch Technique

This response is based on the assumption your right shoulder is the one that is starting to bother you. 

When I coached and a swimmer commented about this, it was almost always due to 2-3 things they were doing.  Applying this to your swimming, these three things can be in play:  1) your right arm/hand may be very close to, or even at, the water surface, 2) your right hand might be gliding right of your centerline (meaning not positioned directly in front of your shoulder, and/or 3) you may be over-rotated onto your right side as you breathe to the left. 

Any or all of these will result in the dead zone/delayed catch you mention.  Additionally, any of these positions can place strain on the right shoulder which could be "tighter" because it is your non-dominant side.

These suggestions will increase your self-awareness which is usually enough to improve the situation:

• Ask another swimmer to watch your freestyle to confirm what you are doing.  Otherwise, you might try to correct the wrong thing.
• When breathing, rotate your head and body just enough to get one goggle out of the water.  This will reduce "laying" on your right side.  This assumes your head/neck are aligned so you are not looking forward or backward (this is along the lines of what 67King suggests). When breathing, your body should rotate no more than 30 degrees and your neck no more than 45 degrees (assumes calm water).  Karlyn Pipes describes body movement as "rocking" instead of "rotating" which I find a much better descriptor for body movement.
• When your right arm is extended forward and before the catch, your right hand should be 5-9" below the surface and your elbow should not be bent.
• When your right arm is extended forward and before the catch, your arm/hand should be positioned straight in front of your right shoulder as if your arm/hand is being pulled towards the end of the pool you are swimming towards.
• This one is speculation without seeing your stroke.  It is possible your head is too low in the water.  This happens when swimmers over-compensate in their effort to streamline.  A very low head position puts extra strain on the shoulder - especially if the hand/arm is close to the surface.

Other things to consider:

• I may get pushback on this, there are some drills that are bad for swimmers to do - especially when done in the absence of a knowledgeable coach.  Finger-tip drag, zipper, catch-up stroke, and some kicking drills can cause strain on the shoulder when done incorrectly (meaning not enough body rotation to prevent impingement of the shoulder).  I no longer include these drills because they are rarely done correctly (or cannot be done correctly due to mobility restrictions.
• If you are older and the right shoulder has been injured in the past, you might have arthritis developing.  This is my situation.
• Some weight lifting movements (military press, bench press, flies, dips) put tremendous strain on shoulders.  If you have added these or changed the weight, these could be contributing factors.  Sometimes what we feel in the water has nothing to do with swimming. 

Sorry for the lengthy response.  The best thing you can do is find a knowledgeable swimmer/coach to watch.  Good luck.  Swimming with discomfort is never fun and very discouraging.

This response is based on the assumption your right shoulder is the one that is starting to bother you. 

When I coached and a swimmer commented about this, it was almost always due to 2-3 things they were doing.  Applying this to your swimming, these three things can be in play:  1) your right arm/hand may be very close to, or even at, the water surface, 2) your right hand might be gliding right of your centerline (meaning not positioned directly in front of your shoulder, and/or 3) you may be over-rotated onto your right side as you breathe to the left. 

Any or all of these will result in the dead zone/delayed catch you mention.  Additionally, any of these positions can place strain on the right shoulder which could be "tighter" because it is your non-dominant side.

These suggestions will increase your self-awareness which is usually enough to improve the situation:

• Ask another swimmer to watch your freestyle to confirm what you are doing.  Otherwise, you might try to correct the wrong thing.
• When breathing, rotate your head and body just enough to get one goggle out of the water.  This will reduce "laying" on your right side.  This assumes your head/neck are aligned so you are not looking forward or backward (this is along the lines of what 67King suggests). When breathing, your body should rotate no more than 30 degrees and your neck no more than 45 degrees (assumes calm water).  Karlyn Pipes describes body movement as "rocking" instead of "rotating" which I find a much better descriptor for body movement.
• When your right arm is extended forward and before the catch, your right hand should be 5-9" below the surface and your elbow should not be bent.
• When your right arm is extended forward and before the catch, your arm/hand should be positioned straight in front of your right shoulder as if your arm/hand is being pulled towards the end of the pool you are swimming towards.
• This one is speculation without seeing your stroke.  It is possible your head is too low in the water.  This happens when swimmers over-compensate in their effort to streamline.  A very low head position puts extra strain on the shoulder - especially if the hand/arm is close to the surface.

Other things to consider:

• I may get pushback on this, there are some drills that are bad for swimmers to do - especially when done in the absence of a knowledgeable coach.  Finger-tip drag, zipper, catch-up stroke, and some kicking drills can cause strain on the shoulder when done incorrectly (meaning not enough body rotation to prevent impingement of the shoulder).  I no longer include these drills because they are rarely done correctly (or cannot be done correctly due to mobility restrictions.
• If you are older and the right shoulder has been injured in the past, you might have arthritis developing.  This is my situation.
• Some weight lifting movements (military press, bench press, flies, dips) put tremendous strain on shoulders.  If you have added these or changed the weight, these could be contributing factors.  Sometimes what we feel in the water has nothing to do with swimming. 

Sorry for the lengthy response.  The best thing you can do is find a knowledgeable swimmer/coach to watch.  Good luck.  Swimming with discomfort is never fun and very discouraging.

"I may get pushback on this, there are some drills that are bad for swimmers to do - especially when done in the absence of a knowledgeable coach.  Finger-tip drag, zipper, catch-up stroke, and some kicking drills can cause strain on the shoulder when done incorrectly (meaning not enough body rotation to prevent impingement of the shoulder).  I no longer include these drills because they are rarely done correctly (or cannot be done correctly due to mobility restrictions."

I appreciate your saying this.  I do the various variants of catch-up by myself all of the time.  I don't have shoulder issues typically, but I am guilty of just "going through the motions" of most of the drills I do.  I have started implementing the underwater recovery drill some, mostly in lieu of the hinge drill.  But I should make a point to focus on my movements on the rest.  Again, thanks for bringing up this.