You, by no means, need to see a doctor ... that is just plain ridiculous. As you said, you are sore ... you've injured your muscles and it is no big deal.
You can wait about 3 days and the soreness will subside. OR ... the BEST THING to do is to get back in the pool and swim more at a nice easy pace. The soreness will likely go away within a few hours.
You should also take some ibuprofen (Advil is a brand name) or, if you're old enough, aspirin as both are anti-inflammatories (acetaminophen - Tylenol is a brand name is NOT an anti-inflammatory). They will relieve the pain and aid in healing.
That advice is true for all soreness ... do what made you sore to begin with, only do it at a light level ... even soreness from weight lifting.
Contrary to Casey's statement that sore muscles rebuild stronger ... they do not. Electron micrographs (pictures taken with electron microscopes) the micro-tears that occur do not heal to make the muscle stronger ... they actually weaken the muscle. Such a comment (like Casey's) is a very old concept that, unfortunately, has not left the lexicon and was debunked about 10 or 12 years ago . The damage from soreness, however, is not major but should still be avoided.
Muscle hypertrophy (enlargement) is caused by an increase of certain substances (proteins named actin and myosin) in your muscles, not from tearing them.