The main thing is: don't count on this resolving itself somehow, or that the amount is too small for tax authorities to notice. Debt accumulates over three years, and the system will eventually catch those deposits in your account one way or another. Fines and penalties hurt a lot more than just paying your taxes on time.
Technically yes, you need to pay 13% personal income tax on the rental amount - it's income, whether you're renting out a room or a whole apartment. But there's one important thing: if you've owned the apartment for less than three years, the tax is calculated on the full amount; if it's more than three years, you can apply a deduction of 1 million rubles. You have three years, so you're already in that bracket and can significantly lower your tax base.
The best option is to register as a self-employed person or sole proprietor, draw up a rental agreement with the student, and start paying taxes. Self-employed registration is relatively straightforward now - you get the app, register, report your income, and pay 4% tax (instead of 13%). Plus you get documentation of legality, which the student might need for her dorm or documents. Better to sort this out now before penalties start piling up.