Just recently I was able to get myself to start a diet and sit less, so I'm in your same situation. I'm still Pre-T, Pre-Op, Pre-everything actually, and I have a huge chest so I've never really tried to jog or run outside, it fuels my dysphoria too much. I've been considering a gym membership since working out in a place with just four/five people wouldn't make my dysphoria be that bad, but I'm still worried anyways. The hoodie is a great idea, I might consider it (with a sports bra)!