By HUD, I think they mean the section 8 program overseen by HUD (HUD stands for Department of Housing and Urban Development). You would probably qualify for section 8 housing (thru HUD), depending on your income, but in many (really most) areas teh waiting list to get into the Section 8 program can be many years and anytime a single parent applies to the program they will likely jump ahead of all non-single parents in the queue (assuming here you aren't a single parent). So, it might be a long shot ever getting assistance via the section 8 program but really not much harm in applying anyhow.
Sounds like you have a decent deal even paying $275 so I suggest you get the rest you owe quickly, pay the back rent and then keep up with your payments or you'll be out on the street very soon. I also suspect that short of losing your job your rent won't go down (and the income you lost would be far more than the rent saved) so expect that $275 to never go down, probably its going up, eventually.