You definitely have the right to ask, as every year you are entitled to a raise. Nothing bad can come out of trying. And you never know, maybe you’ll even get it.
Another tip: always ask for a raise more than you want. Ie, you want another 3 grand a year, ask for 5. This way, hopefully you’ll get the three you want (you might even get the 5, but I doubt it if your place is struggling.)
Good luck!