Asprin Regimen for a Dog?

Well my dog has brain damage from a high fever when she got sick. Now she does not walk well she more or less waddles about. One person even asked if she was a male dog that just got neutered because of the way she walked. She seems really happy but has them depressing moments when she wants to play and ends up just falling to her stomach. We give her asprin like maybe once or twice a month when she is having really bad days. I just think that what if she always took asprin and always felt as nice and comfortable. My mom refuses to go to the vet and ask for pain medication so i kind of am taking this upon myself to find a way that does not require a vet visit. So can dogs go on an asprin regimen or any of them other pills that do not need a prescription?