I sometimes get elbow pain while swimming freestyle, too, although mine is actually caused by my shoulder. Anyway, first I would say to check your form/technique to make sure that's not causing your problem. To treat your elbow, ice it and stretch/strenghen it. I found some exercises on WebMd and checked them out with my physical therapist and they are good exercises to do and they are. Good luck!
I don't have an answer to your actual question but note there are two styles of soreness in the elbow: tennis and golfer's elbow. You may find that a glucosomene suppliment may assist in relieving the joint pain after a week of taking it.
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