You might want to check out something called 'drownproofing'. It's pretty simple. With your body vertical in the water, let yourself sink, your arms and legs spreading out as you drop, then push your legs together and your arms to your sides, You'll go up. Grab some air, start exhaling once your nose is below the waterline and relax. You should be able to keep it up for quite a while

This is the first thing I teach kids in the water.

As you're a yoga teacher, you might be fit enough that you don't float (yeah, me, too). Whether or not you can float, drownproofing works - and it'll make the water a much less scary place.