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These recurring bone spurs you are encountering are called exostoses. Because of the specific location of yours they are called buccal exostoses. You can see a picture of a more severe case with description here:
Normally these do not break through the skin and require no treatment. However, since yours tend to do so, you should consider having them removed professionally by an oral surgeon, who can smooth these extra bits of bone flush with the normal jaw, rather than just breaking them off, leaving a jagged surface, which promotes their regrowth. You can find the contact details of an oral surgeon near you by following this link:
There is no relation between these exostoses and the skin problem you are having on your face.
I hope this answers your question. If you would like to discuss this further or have any additional questions, please reply to my answer and I will get right back to you.
Sincerely, XXXXX XXXXX DDS