What causes small raised lumps on the sides of the cheeks inside?

Dozens. Dozens of causes. Most are benign. Many are temporary. See your Dentist, a Periodontist, or an Oral Surgeon for differential diagnosis and, if necessary, treatment.
Some lumps normal. Whether the lumps are painful, bleeding, the color, and the size are all important factors in answering your question. Most of the time these are normal changes in the mouth tissue that resolve. if painful, avoiding high acid foods/drinks may help. Smoking and any tobacco use will slow healing and lead to tissue disruption as well .
Lumps inside cheek. Most common is mucous cyst. Other clauses are malalignment of teeth and constant biting on the inside cheek. If there is sore ulcer spot and it should be biopsied. The closest to consider will be Herpis infection.