Can i get a settlement if i get injured at work?

so a month ago my middle tip of my finger (from the nail up) got caught on the crease of the door and someone shut it. and it ripped open and broke a bone and had to get stitches, a month later it still looks kinda gross and will def be somewhat deformed looking.ive never had a problem like this before and my job isnt really telling me anything they are just making me do "light duty" work because they said i dont qualify for work comp (im a server by the way) because i work part time. can someone explain to me if i get get a settlement (which will help ALOT) or what do i do. i did report the accident though right away