Welcome to the forum, horsegirlxx!
It can be very challenging to balance school, horse ownership, and other obligations, but it can be done!
As RD11 said, a 4 year old is probably going to need more in the way of training than your school obligations may allow. Depending on your horse's exact level of training, it may definitely be worth it to investigate some pro help anyway.
What matters with training horses, though, is quality, not quantity. Especially youngsters and greenies - they often progress much faster with a couple of short (15 minutes-ish) sessions a day rather than one hour-long workout. It's easier on their bodies and their minds, and in terms of your schedule, you could do a short session in the early morning and in the evening. And remember, every interaction trains the horse. If professional training is not an option for whatever reason, as long as your gelding's needs fall within your training ability, it can be done. Something else to consider might be some sort of lease to a more experienced horseman looking for a fun training project - assuming that your boy just needs miles, and doesn't have any problems that need addressed.
6:45 a.m to 5:00 p.m. is one heck of a long school day, and I expect that you'll have homework as well. Do you have a long bus ride? You can use that time to get started on homework assignments. Even try taking your homework out to the barn - find a comfy spot against a tree in your horse's pasture, and combine homework with bonding time. Your weekends offer prime time to handle bigger jobs and longer rides, like an in-depth grooming/massage, deep-cleaning tack, and trail rides or lessons.
It'll be tough, and it will take real commitment to juggle everything, but it can definitely be done! Good luck!!