You can develop impressive squat numbers without a belt. It just depends on if you train your body to lift with, or without, a belt.
On that same note, it is not a bad thing to use a belt either. It just depends.
My recommendation is that if you are serious about your lifting, buy a quality belt that you will have for a long time and see if you like using it. I go through phases where I use one, and don't use one. Most people find a considerable increase in their squats number with a belt.
However, your 225 goal can certainly be realized without belt, so don't let that be what is "holding you back" in your mind. Also, your low back pump is not the absence of a belt, but rather a form issue or weaker muscle group that needs to get stronger probably.