It may be difficult to think about telling your parents, because there is still a lot unknown. You don’t have a diagnosis, nor a prognosis. At some schools, a significant percentage of students receive mental health/counseling services. While some students find it easier to ask for professional help than others, it is much more common than not for these students to have some level of trepidation/concern before choosing what / how to discuss this topic with their parents.
The simple fact that you are taking advantage of the counseling is a very good step for you. Right now, your post reads in part as though you are trying to predict how the entire process plays out until you are completed “cured”. Please understand that these issues are almost never that easy to predict.
There are perhaps as many kids who don’t need to get on medication as a result of MH counseling as not. I don’t want to downplay your situation, but have you considered telling your parents at various milestones - and treat many of them as celebrations. I don’t know your parents, obviously, but I have not met many parents who would truly be upset with a child who has decided to get help. There might be a little shock, but the biggest reaction is more likely concern. When you tell them you’re getting help, you start to tell them by thanking them for helping to prepare you to know right from wrong, and how to make good decisions. You know they want the best for you, as they have (often or) always shown that. They helped you pick a good school that is right for you. Your coach or one of the advisors, etc. has reminded you that these services are offered at school because there are a LOT of kids who benefit from them. So you want them to be glad for you that you are going to get the help you probably need.
Depending on your relationship with your parents, you might try to add a dose of humor along the way - stupid jokes can break a fair amount of tension. Things like - “next semester send me a shirt with a smaller collar because I’m getting my head shrunk.”
You can tell them you were concerned about telling them, in part because you don’t know how this will play out. You don’t know whether or not you might be better off with medications, or how much any of it will cost, but for now, you are going to look into this while the first x visits are free/covered by the school. Because after all, your parents taught you the value of a dollar, so taking advantage of something free is a good way to determine if it is right for your situation.
You don’t have to share everything with your parents, but if you give them small pieces, sandwiched around how much you appreciate everything they’ve done for you, and that you know they will always be there for you, and you wanted to tell them in advance you really appreciate the respect you know they will give you as you work through this process. You are glad that when it comes to this issue, you are telling them in advance with respect for them as adults, and as a young adult yourself you appreciate them treating you as an adult. And most of all, you thank them for understanding that since this is about you - not them, there may be times when you might not be ready to talk. But after all, it’s not like you are about ready to quit college and get a job selling weed. When my D came home from college on her first break, her stock answer to anyone who asked about college was “okay, I guess, but I’m not pregnant by my professor…yet”
If you tell them this, it lays the groundwork for what may come down the road, but it also disarms them of any accusatory/probing questions that you might not be ready to deal with.
I really wish you the best in your next steps