The side effect that is most of concern is that there may be skin thinning and skin dystrophy if the jabs are performed too frequently over the same area.
There are other treatments available for small bumps, and you should consider them. This includes topical applications.
There are also other more permanent solutions such as oral Accutane.
Bearing in mind of course that each of these can also come with their own side effects, and you should weigh this up with the doctor treating you!