How to cook better cookies despite a terrible oven?
As suggested by Catija, moscafj and Ecnerwal the first thing you want to do is get a oven thermometer to verify that the temperature you're setting is the one you're actually getting. If possible you might should to bring it back home to see how well your home oven is calibrated. It may be the case that your home oven is slightly off in one direction and your dorm in the other direction so you might need to make a bigger adjustment than just testing your dorm oven would indicate.

That said, it sounds like your problem is that you're leaving the cookies in the oven for too long. Chewy cookies are basically under cooked cookies, you want to take them out of the oven when they're golden brown on the outside while still soft in the middle. Differences in lighting and glass between your old stove and the new one might make it harder to judge when the cookies are done, causing them to appear less browned then they actually are. Also cookies will still cook a bit while cooling on the counter, hardening up, so you're aiming for cookies that are a bit less done than you want in the end.