You say apartment in a college town - I’d guess this room is smallish and cube-like dimensionally? Forgive me if I’m off base with my assumption, but if it’s anything like the college apartments I’m familiar with, the kind of space-optimizing dimensions these places have make things more difficult to deal with right off the bat.
You’re dead-on with panels and tiles like fiberglass and foam being good for high-frequency echoes and flutter, especially at first-reflection points, but with the room type I’m again assuming you have, Mr. Kuras is correct about the low-end issues that are probably present, which require trapping. Addressing only high-frequency and echo problems can make things even worse if you’ve got low-frequency issues that remain unaddressed. It’s kind of like adding ketchup and mustard to a hamburger bun that’s missing the meat
I say this all in general terms as well – if you can post dimensions or even run some room tests, I’m sure you’ll get some responses that are more tailored to your particular issues!