I can't read a text at near distance and my eyes get tired quickly, should I go to a doctor and could it be farsightedness/nearsightedness?

Iam farsighted and have experienced the same thing. Glasses give me corrected vision at all distances. Get a proper exam with an eye doctor. A school nurse is not set up to check for this.

Go to an optometrist. Yes, it could be one of those.

You are probably far sighted. I'm personally near sighted and I went and got glasses so I can see far. I don't wear them all the time. I also have astigmatism which means the eye is shaped oddly. It's a pretty common thing and you may have it also. Not a big deal and doesn't even need corrected unless you want to get glasses or it effects your daily life. Good luck!