Tl:Dr: chemical burns, not very bad, quit immediately, didn't go to the hospital, my family is pressuring me to get worker's comp but I'm not even sure if I can.

Ok so, it was a temp job, I was not told at all that it would be a job where I'm around hazardous chemicals and I wasn't really comfortable with it, but I needed the job. In my third week, a machine didn't cap a bottle right, and the spinning table that it was on was being very jittery, so it was sloshing around. When I tried to put a cap on it, it splashed upwards, got on my face, up my arms, and all over my shirt.

Now they did provide me with gloves, glasses, and an apron, but the apron didn't cover a lot, the chemicals burned through my shirt, got all over my arms, and a bit on my forehead and chin.

The burns weren't that bad honestly, but I was in a bit of shock, it hurt like hell even after wrinsing off, and they wanted me to get right back to work since we were behind schedule, so I just quit then and there, wasn't dealing with that.

Now I don't think I need to go to a hospital, the burns don't hurt anymore and this literally happened yesterday, they aren't very bad at all. But my family won't stop pressuring me into filing for worker's comp and I'm not even sure if I can do that. I quit without notice immediately when it happened, it was a temp job on top of that. I didn't go to a hospital. I just went home. My family is telling me I should get money because the PPE they provided wasn't adequate...

I really don't know what to do here, really I just want a yes or no, if people here tell me I should try to get worker's comp I'll start looking into the steps and what to do, but if people agree that this doesn't warrant that I'm just gonna leave it. I want opinions.