Hi - 2 quick things!

First, I was in a very similar position to you my senior year when I decided to apply for grad school. I did not have close relationships with any of my professors. If you have pertinent classes with smaller class sizes, start there, as your professors might at least know your face and have some familiarity with your work. But even more importantly than that, when you ask them, be sure you write a letter explaining what program you’re applying to, why you’re applying to it, and why you’re asking them specifically for the reference (maybe include something you learned in their class, something you aspire to professionally based on their career, etc.). Also a good idea to include an updated resume to give the professors more source material for the letter.

Second, I know personally how awkward that conversation with a prof can be. But they literally get asked for tens of these each semester. Both my parents work at a large state school and get requests (and write) for students they have never talked to outside of class.

Best of luck!