"Here are my measurements. Bust: 38 3/4, Underbust: 36 2/4, Waist: 35 3/4, Hips: 40 2/4, Height: 5' 7, Weight: 183 Lbs, Age: 17"
I started nearly your same stats. I know the feeling of being big. It's possible to lose the weight, even quickly. I'd get the weight under control first, before going on HRT, as it'll be harder to lose when on T blockers. Anyway, easiest changes are add walking, and cut meals in half. Go ahead and order the same food you love, but cut it in half and save the other half for another meal. once your body has adjusted to that start having a salad every now and then, not every meal, since you'll get burned out. Lastly bread is your enemy. It tastes yummy, but try to intake as little as possible. If you get a burger, take to bun top off and toss it. There 1/2 the bread!
Anyway doing these simple tricks for me allowed me to get down to 160 in two months. It's not a huge change in diet, mainly a lifestyle choice on how much to eat and a little exercise. Oh, for walking do a mile a day, then on the weekends do several. That's about a 30 min walk weekdays, and a couple hour walk weekends. It's okay to go slow, take in the sights. Gotta make the walk fun, not just around a track, that's work!
You'll get that figure you want faster than you think. Weigh yourself daily. When you see results from the scale, it'll be the encouragement you need to continue.