Meg,
Your situation is exactly like mine when I was younger. I was a softball/fastball pitcher growing up, developed pain throwing and then it just kept hanging around and didn't feel stable. My OS initially thought I had a labral tear, but MRI came back ok and figured it was the front of the capsule that had stretched out from repetitive motion. I ended up having surgery when I was 18, on my right throwing shoulder and they did a capsular plication (tightened the ligaments) arthroscopically. I was in the sling 6 weeks and did a throwing program and was able to get back to throwing again...to this day I can still throw. I have had 7 shoulder surgeries now (I'm now 27), with that one successful one on my right and 6 on my left...it's my left shoulder being the reason I had to give up playing. If continuing to play is something that is going to be a big part of your future, well sometimes you have to play the game of risk to keep it going, but you also have to be ready for things to not go in your favour. I worked really really hard at my rehab and had a great therapist who knew the mechanics of pitching that got me back. The younger you are, the greater your chances of success because the tissues heal better. Now, I will never ever tell someone that they should do the surgery, that is a decision that needs to be made by you, when you are ready and feel it is your only option. I wanted to share my experience with you tho so you know that it can be successful.
In my opinion tho, even tho it sounds as tho you've stretched out the front...I would always encourage another opinion (usually 3 opinions are good...a third being a tie breaker of sorts). This is a very big decision, you have a right to get as much information as possible and remember, at the end of the day, you choose a surgeon you are most comfortable with and trust. You don't have to go with the first one, even if they do have the best resume. Another thing, when you are sitting around keep a pad of paper with you to write down any questions you want to ask the surgeon or your PT (a lot of people forget them when they see a doctor). Some good questions to ask in this case would be...
Do you think instability is my problem as opposed to a SLAP?
What are my chances of PT correcting that problem?
What do you do in terms of surgery to fix that problem? Arthroscopic?
What is your rehab protocol for this? Sling time? Range restrictions after surgery?
What is the average return to sport timeframe for that procedure?
What are the possible complications from the surgery? Short term and long term?
How many of these types of surgeries have you done and feel comfortable doing?
Is this best done when I am this young or preferred to be older for a better chance of a successful surgery?
If I have this surgery, return to pitching...what are the chances this problem could recur/come back?
Those are some good questions to ask when you see any surgeon...in the end, they are the ones that have to gain your trust to 'earn your business'...to do that, they need to be able to answer those questions.