Newbie Question

I'd love to hear from some experienced swimmers. I'm a woman in my 40s who just started swimming off and on again this year for exercise. I swim freestyle, and took a class about 10 years ago to learn it. This year on two occasions when I was not using a nose clip, I must have inhaled a little water, because it felt like I could not breathe in at all -- like my throat had closed. I tried to relax, and in both cases it lasted maybe about 10-15 seconds. It is super scary when it happens. I know that this is likely a protection mechanism of sorts, but I am a little perplexed. It is not like I was swallowing lots of water or anything -- but I do think both times I was trying to swim without a clip, and so I must be doing something wrong with my breathing. So, how should I deal with this? It has made me afraid to swim, b/c when I read about laryngospasm all I get are all these links about dry drowning, etc. Does this happen to everyone on occasion? Any advice would be appreciated.