Tough situation here. Good on you for asking advice. You are correct that officers and cadets cannot date enlisted members of their service nor any other service. This is spelled out in the Uniform Code of Military Justice (UCMJ). The UCMJ lays out the laws of the military.
USCGA also requires cadets to enter and remain unmarried throughout their time in New London. This is the same as the other Academies.
The military makes you grow up quickly since you make a lot of life decisions early on (career, financial, etc.).
My best advice is to have a long discussion with your girlfriend about both of your career aspirations and how they relate to your relationship. In essence, both have to figure out what is more important: your career or your relationship. I don't just mean finding a different career. What I mean is don't fall in love with your plan. You can still go active duty (albeit delayed) by going through OCS and then it's fine. You can stay dating while going to college as a civilian. You'll both be officers and all is good. Or, you both can enlist. Or, you both can do college as civilians and go through OCS. Plus, if you end up getting married, co-location is a thing. Plenty of ways to accomplish what you both ultimately want (CG service ad staying together), just not the ways you've envisioned.
If both of you are unwilling to compromise on your career goals (as in both of you have decided to enter the CG in your chosen ways), then she may not be the one for you. That is part of having adult relationships: compatible career aspirations (or at least willingness to compromise). Very tough since 3 years is a serious relationship. Making it that far means y'all can compromise on things, but career stuff isn't really a variable until college. So career talks don't seriously happen until about this time.
I hope that helps a bit. Don't mean to come off harsh if it's taken that way, just want to be transparent. Best of luck!