You may need to elaborate a bit more on what your are trying to achieve; it looks like your post is missing a bit of backstory. It sounds like your concern is keeping your personal business and school activities separate, though.
Switching away from Google is overall a good thing for privacy, but if your goal is privacy from your school, not from Google itself, it makes no difference who you want to use for email.
Creating an additional account on your PC is not detrimental to privacy; in fact, some might argue that having a separate account for separate tasks is actually a good thing. I have multiple accounts on my servers, depending on what/who needs to log in. It doesn’t hurt to do the same on a desktop PC or laptop.
Simply accessing school resources on your PC isn’t going to send the school your personal information, browser history, pirated movies, whatever. Clear your browser cookies between sessions if you’re concerned. Better yet, just set your browser to automatically clear cookies when you close the window, and make sure you exit the browser when you’re done with school work.
Do you really need to use your school e-mail for anything other than school? I have a work email, but I only use it for things that are directly related to my job.
What you’re saying doesn’t really make a lot of sense. A lot of people here are probably happy to help you out, but you’ll need to be a bit more clear on what your goal is. I get the impression that you’re concerned about your school having some kind of privileged access to your computer because you check your school email and work on school assignments using personal computing resources. That’s not something you need to worry about; it’s really not how technology works. Logging into your school’s online portal doesn’t give them access to your files any more than buying something on Amazon.com lets Jeff Bezos browse your system.
If you’re really, REALLY concerned about privacy, just set up a VM using VirtualBox (it’s free and easy) for school stuff and continue to use your computer as you would normally. If you’re already comfortable re-installing Windows, then you absolutely will be able to set up a simple Windows VM. To be clear, I wouldn’t consider this necessary, but if you want to do it for peace of mind, then you have nothing to lose.
This situation becomes vastly different if you have a company or school-issued computer. In that case, then I wouldn’t use it for anything other than strictly business (or school)-related activities. Given the fact that you’re able to reformat and add/remove accounts, though, it doesn’t sound like you’re using a computer managed by an IT department.
On a side note, if your school did some how manage to gain access to your personal computer without your permission, find information that was detrimental to you, and somehow use it against you, I would ask you two things:
What the hell kind of school are you going to?
Do you like money? Because you and your lawyer are going to get a lot of it.