I'm going to complain to my boss about getting more work than another employee
Are you getting paid more than other worker?
I don't know if I do but the other guy isn't even a good worker
If they aren't doing their share and are doing what they do get poorly, that's not right. It seems like your boss already knows they aren't cutting it since they give you more work, but it's still okay to approach them about this situation.
Fine but I'm not sharing it with my manager
You can always ask for a higher salary if you are doing more work. A very simple solution to a complex problem.