After your swim rinse your clothes and wetsuit well. Regardless if it is chlorine from the pool, salt and sand from the sea, or mud from a lake, it all can rot your suit. Take a shower in your wetsuit to rinse the outside. Then take it off and rinse the inside. Now put it on a hanger in a well ventilated space. Don't use any shampoo. It can damage the wetsuit or your lycra rash shirt.

Delicate Smoothskin Wetsuits

Most wetsuits have a soft outer nylon fabric cover. Smoothskin suits do not. The advantage is that when you're out of the water it just runs off, avoiding evaporation chill. The downside is that it is more delicate and can get damaged.

If you really want to protect a smoothskin suit when scuba diving, wear a one-piece nylon stingersuit over the top of the smoothskin suit. That way you are much less likely to rip or tear it on rocks or when taking the scuba gear on and off. Would have to be a slightly larger, as a well fitting nylon suit over a 3mm wetsuit may still be slightly too tight.

A cheaper and more robust alternative:
Protect your wetsuit with old clothes. Wear a long sleeve top and jeans or cargo pants over the wetsuit. It may create a bit more drag but is more robust than a stingersuit and has pockets for small stuff and keys.