Waterproof chest strap?

Just a note-Bluetooth doesn't work underwater so a lot of HRM are waterproof and you can wear them in the water, but they won't be able to connect to any watch/phone/device to see the info (if that's important to you while working out).

Wahoo tickrx has a memory function that will record your HR data when you're in the water, then sync your workout data with your phone later. If you're doing a workout on land, It will sync live with your phone/watch via BT (and ANT+) and display current info (that's not what you asked about, but in case you want something that will work in more than one setting).

Polar HRM that transmit via "gymlink" can transmit underwater to a watch/receiver that receives "Gymlink."

I believe the latest round of Garmin Tri and Garmin Swim monitors are also waterproof/swim capable but I believe you will need a suitable Garmin watch in order to use the info. This combo will likely put you over your budget.