Injury... hoping it doesn't mess up my swimming

Hi all, After a run during which I tripped and fell, hurting wrist and knee, I had a lovely open water swim (about 2400m, topping off the weekend total to about 12k--doubled this a.m.), but did feel some discomfort in my wrist. I chalked it up to the fall, but now it's evening and the wrist still hurts (though I've been icing and taking tylenol--allergic to NSAIDs). With the Tylenol, I seem to be doing okay w/ typing this, although with slight discomfort. But reading online, I'm seeing all kinds of worrisome stuff, such as that I should get to a doctor, get an MRI, maybe have surgery and at best, 10 days to two weeks of rest. (REST?? WHAT'S THAT?) iI'm training for a 5.4 mile open water swim, so I'm putting in some serious yards (shoulder is starting to feel it too but I figure a few appts w/ my chiro guy should help that--he does ART which is torture but helps). So my question: Have any of you trained w/ a hurt wrist? Does the fact that I could still swim bode well (I hope!). My swim is 7/22, and I want to be ready and don't want to stop training! I'll have my doctor take a look tomorrow, but sometimes she rules on the conservative side. I have taken falls where the wrist came back pretty quickly so I'm hoping that happens this time. Fingers crossed Thoughts? (Also healing vibes/prayers welcome!)