First off, congratulations on your upcoming high school graduation! 😊 I'm sure you must be very excited to start HRT and move out on your own.
The development of your breast ducts will happen pretty quickly early on. This will result in your nipples increasing in size and protruding noticeably from your chest. This is normal, breast fat will grow to fill in the shape around your breast duct and once enough of it has grown, the nipple will not appear to protrude and will instead be at the apex of the breast. The development of breast fat takes a longer time than breast ducts though. Certainly if you're on HRT starting in May, by July and August your breast ducts would be developed enough that your nipple would be noticeably larger and raised without a shirt on.
I recommend familiarizing yourself with the tanner breast development scale which can give you a bit more of an idea how this development happens. You could wear a shirt while swimming and a sports bra underneath it. Though depending on the material of the shirt and the color, it might be noticeable that you're wearing one. You may have to find ways out of swimming later in the summer, like saying you don't feel like it or something like that.