Swimming after workout

First things first, it is very important to 'aptly' warm your body up before hitting one of the two! It is as important as washing your hands before a meal. Free hand exercises, a good jog or stretching out your limbs relaxes your muscles for subsequent activities and reduces wear 'n tear.

Now, I am assuming that your primary motive is to gym (than to swim), it is generally considered better to go the gym and then go for the swim. 

In the gym, you are subjecting your muscles to sudden and heavy weights or forces. Your heart is pumping more blood. Your muscles are stretching more than usual, your ligaments are twisting more etc. In short, your body is tiring. 

Swimming, after a tough gym regimen, helps your body soothe. It is important that you let your body relax and recuperate. Do not over-swim. The sole purpose of swimming after gym to re-energise. Over-swim kills the very purpose. Mild swim helps your stiffened muscles to ease out and rejuvenate. And this is the best for your body in the long run. 

Bottom line is, whatever you do, give your body ample rest. Relax. Eat well.