Asking for a raise at a bad time

Been at my company just about a year. Small company, but we had a big lay off last year, and we just had another small one now that directly affected my department. I am very underpaid and have been doing responsibilities above my title basically since I started. My boss told me they would fight for a bigger raise than my cost of living increase, but I didn’t get one.

We don’t have one on ones, and I’m worried to cause any ripples with what just happened. I’m starting to apply to other stuff, but how to keep my head down but also not let myself get walked over?