Hi Hannah,
I think a lot depenRAB on your age and how much more growing you have to do. Early intervention is the best. I wouldn't go the chiropracic route. They can't cure scoliosis, though some will claim that they can. I have a friend with a granddaughter in California. The granddaughter had scoliosis and her parents, who were separated, couldn't agree on treatment. The mom wanted her to go ahead and have surgery. The dad wanted her to go to a chiropractor. They agreed to give the chiropractor 6 weeks to show some improvement, any improvement at all. They took her to two different chiros three or more times a week and after 6 weeks she had gotten significantly worse. She had the surgery in Deceraber and is now perfectly straight, her ribs not even deformed anymore, and has no pain at all.
PT will help you to strengthen your core muscles, which is important with a bad back, but it won't correct the scoliosis.
I have a severe scoliosis which didn't get treated early enough. I have a lot of complications now from not being diagnosed and treated when it started. I will never work again and I have pain everyday. I'm 49.
I have a son who also has scoliosis, thanks to me

(). He was diagnosed at age 14 and wore a brace for 12 hours a day for several years. His curve did get a bit worse while in the brace, but I believe it was the brace that kept him from getting as severe as I did. He did not need surgery and has no pain.
I recommend that you find a good orthopedic spine surgeon who has done a fellowship. If you're under 18, go to a pediatric orthopedic spine surgeon. Time is of the essence! You want to stop this in its tracks if you can. That will be your best bet for less pain as you get older. If your ribs are already showing deformity, please don't wait any longer. I'm guessing that your curve is to the right, causing your left ribs to cave in and your right ribs to be hyperextended. That could cause the heart issue you described. It will also cause restrictive lung disease, which is actually more a condition than a disease, but it means that your lung on the side with the caved in ribs can't inflate properly, so you'll become short of breath more quickly than normal.
Please come back and let us know how you're doing. Don't be scared. You've already accepted that you need to deal with this. Now take the bull by the horns and find a good doctor and make an appointment.
Hang in there, sweetie! Been there, done that! You'll be stronger for it!
Blessings,
Emily