This may sound totally lame, but I'd look for a class. You really want to learn decent form for all the (common) strokes before you have bad habits to unlearn. It will also force you to get comfortable in the water, and after you've spent money on the class, you'll be compelled to keep it up.
This is very good advice. Form is extremely important, commitment too if you want it to amount to anything. Of course, just learning to be confident that you can swim and not drown is a real accomplishment, but it's just the start if you are doing it for fitness.
This is very common in swimmers. I had the same thing (ended up being a SLAP tear). Suffered from it for years and when I finally went to the Dr and explained to him the symptoms the very first thing he asked me was "did you swim a lot growing up?"
More for the OP, that's not something you are really going to have to worry about as you are just taking up swimming now (although anything can happen I guess). And yes, swimming will kick your ass.
I used to be very into running but I had a sudden problem with one foot and had to give it up. I went to a sports clinic and swimming was suggested. I immediately went to a local public pool and started swimming daily for aerobic exercise. I was already extremely experienced in swimming, so that wasn't an issue. I was soon doing 1/2 mile/day and then 1 mile. One day I went "why not 2?" From that point on I was swimming 2 miles/day, 7 days/week (and that continued for about 10 years). I soon joined the Y (a lot cheaper paying by the month than by the day) and soon became their most dedicated swimmer. I'd pass practically everybody and I guess I was something of a terror. I used a snorkel to alleviate pain in my neck from thousands of turns. They called me "snorkel man," I learned later. Not too long after joining the Y I started also going in the weight room before my swims. After a while I was in there for 1 1/2 hours before my swim, and my swims were down to under 55 minutes for 2 miles, I almost did 50 minutes one day, shy a few seconds. I'd always take my 1/2 miles splits with a wrist watch, keep my times in a journal.
I'd have aches and pains from time to time but just swim through them as best I could, it would ebb and flow but one day the pain in my left shoulder wasn't bearable and I cut my swim short. From that day onward I was never able to really swim again. It was just before the Y completed its new Olympic style pool, so that was a bummer. A few years later an orthopedic shoulder surgeon was unable to determine exactly what was wrong with my shoulder, but everything else having failed to help (shots, physical therapy), he said I had the option to have him go in arthoscopically and clean up the joint and see if he could find anything he could repair. They found a "type 4 SLAP lesion" (superior labral anterior-posterior lesion, a type of labrum tear) and repaired it on the spot. The recovery was a slow process, physical therapy and a lot of stretching and gradually increasing range of motion and strength exercises. I'm pretty OK now, do the gym stuff regularly, but don't think I'd chance trying to swim balls-out the way I used to. I was very aggressive. One day a guy was in the pool who was significantly faster than me. Aside from him I didn't often encounter other swimmers in that pool who came close to keeping up with me, much less pass me. I didn't like slowing down for people and would try to pass people whenever I could without being rude. I got called into the office a few times because of complaints, however.
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