My heart rate won’t show up during a swim workout

This is actually pretty normal. Contained in this link, is the following statement:

• Pool Swim: When you start a workout, be sure to accurately set the pool length to help your Apple Watch measure laps and distance. GPS isn't used during a Pool Swim, and water might prevent a heart-rate measurement, but calories, laps, and distance will still be tracked using the built-in accelerometer.

Here's the link --> Swim with your Apple Watch - Apple Support

You could try to strap the watch to your wrist tighter as what is likely causing this is water getting underneath the heart sensors on the underside of your watch.

Also had to make some minor adjustments to the band when swimming to get it to record the heart rate. You might try the other wrist to see if that will help.

Once you get it right, it works very well with heart rates, type of stroke your doing, speed, distance and numbers of strokes