Hi manatree,
As jermy4 mentioned you are in a very low budget range but the good news is that you are looking for a twin which are less costly than the larger sizes.
The best place to start your research is the mattress shopping tutorial here which has all the basic information, steps, and guidelines that can help you make the best possible choices.
As you mentioned … your budget isn’t large enough to include a latex or latex hybrid mattress although you are close to the price range for a twin size Ultimate Dreams latex/polyfoam hybrid.
If you are looking in an online direction then Dreamfoam on Amazon has a fairly wide range of different types of mattresses in your budget range (and the 12 in 1 customizable mattress here can be customized to different firmness levels) and as jermy4 also mentioned Tuft & Needle also sells a firm mattress in either a 5" or 10" version that is in your budget range as well.
If you are looking locally then if you let me know your city or zip code I’d be happy to let you know of any of the better options or possibilities I’m aware of in your area.
Phoenix