Why are those bumps around my mouth? Is there a surgery that could flatten them out?

I recommend fillers for to camouflage around the mouth and cheeks to build underlying anatomical support. In our practice we combine sculptra with other fillers "layered" on top and lasers, rf treatments, J Plasma and peels to get the most conservative natural look. Please see a facial sculpting expert. Best, Dr. Emer

The lumps and bumps can be muscle, fat, or a combination of both. Surgery such as lipo may be a bit severe for that area with the risk of more significant contour abnormalities. Non-surgical options such as filler can be used to camouflage the lower depressions so the transitions are more smooth. YOu can also have just a bit of conservative botox placed in to help weaken the muscle and allow it to thin slightly. Hope this helps!Johnson C. Lee, MD
Board-Certified Plastic Surgeon
IG: @drjohnsonlee

Small cannula microliposuction can be done to reduce these discrete mounts of fat around the lip areas. To do is so successfully a microcannula of 1mm must be used.

Filler could be used to address volume loss and lift the face, both of which help the appearance of your perioral area. I would also consider a skin tightening procedure like Thermage FLX as needed. Hard to give you firm recommendations without seeing more of your face. 

 Hi, from the photos these are likely small areas of hypertrophied (thicker) muscle (orbicularis oris muscle).  There is no fat in the muscle that surrounds the lips and mouth, so liposuction would have no effect.  If you would like these mounds of thicker muscle flattened....an expert Botox injector (or using another neurotoxin) can use a diluted solution of the neurotoxin to slowly weaken and cause the muscle to atrophy in those areas.  Caution should be observed in the strength or amount used as too much will make it difficult to purse (contract) the upper lips.  We have used this therapeutic method many times to decrease muscle mounds around the upper or lower lips.Hope this helps.