It sounds like you are in some very similar situations that I was in.
Are you in the States or UK, Canada, Australia or New Zealand?
I was not a gymnast in my youth. My dad was in the 60's for some time as a youth and always watched it when I was a kid. I started to get interested in some bodyweight conditioning through martial arts in HS and as a polevaulter in my junior and senior years. We did some rudimentary gymnasts such as PB swings, pirouettes, candlesticks, chin to levers and our coach would espouse how a PVer had to be part gymnast.
In college I managed to take a tumbling class for a semester and then another by which time I had found a job coaching recreational gymnastics at a super rec gym. Small, maybe 2000 sq feet with a commercial ceiling. Luckily the owner was a german national gymnast and one of the coaches competed at UCLA in her youth. During the tumbling classes I made friends with a guy who was an ex-optional men's gymnast and there was a few ex optional female gymnasts besides cheerleaders.
I started going to regional congress every year and eventually came across
http://www.drillsandskills.com after about 5 years. By that time, I had starting training on my own, reading books about gymnastics at the local libraries. There wasn't much online in those days and it didn't ever occur to me till then to look for stuff.
In 2003, I eventually started working at a competitive club that optional girl's and boy's gymnasts. A lot was learned by just watching them and asking questions or assisting team coaches from time to time. Prior to that I had already done so at another rec gym, but they trained up to L6 in girl's. Still rec-oriented but there was more to be learned by asking and watching those coaches.
You're in a much better position being younger than I was since I started around 20-21. However, this isn't a profession where you make great pay. You may end up having to have a second job or doing this as your side job in the evening.
I will note that I've gym-hopped a few times. Honestly, I don't see making a great living at a recreational gym. If you end up becoming a manager, you're probably making 30-40k tops in the states but perhaps more if you end up becoming a manager at a BIG gym or of course, a gym owner.
College wise, I've known a lot of coaches who get kinesiology or biomechanics degrees. Some, get EarlyChildhoodEducation degrees or SportsPsychology but I seriously doubt ECE will get you very far into the advanced levels of coaching say optionals, L10's, or elites.
Find a coach to mentor under, possibly at your gym or a nearby gym or in correspondence or by visiting their gym. If you have days off, use them to go visit other gyms and sit and watch with a notebook. However, this can sometimes land you a job offer at that gym. Be warned. Sometimes, you may get invited on the floor to watch or help.
USA-Gymnastics also has a level program for coaches through USA Gymnastics University. It's in the works right now and they may only offer L1-3 though they have it mapped out to L5. Gymcert is another option.
Go to as many seminar or clinics as you can, read and watch a lot of video.
Look into the judging programs for either the women's or men's. This can definitely get you ahead in your coaching and you get supplement your income on the weekends. As well, it can establish connections via networking.
Back to gym-hopping. Some owners during interviews will grill me a lot about this. A couple of gyms just had no place to go or were not great places to be which was my fault in working there. Sometimes the pay was dismal or the experience was dismal...or worse, BOTH! You may have to. Though eventually you will want a gym to stay at to build a program or work yourself up in. You may end up having to work at some small gyms in the process that are struggling or don't have a great vision or share yours. I would advise you to stay away from them but in all honesty, sometimes you have to pay the bills or get stuck taking a job at a gym that doesn't pan out.
