Are these undereye bumps milia or syringoma? (Photo)

From your photo, they look more like milia to me. I would see a medical aesthetician who works in the office of a dermatologist or plastic surgeon and can do medical grade peels and high quality microdermabrasion. This may be something you deal with chronically, but there are definitely things that can be done to help it. 

These need a formal evaluation, but I find that clear + Brilliant, Fraxel or viva with microneedling help this a lot.  If they are truly syringoma they need resurfacing or desiccation needle.  Best, Dr. Emer.

Based on the photo and the location the bumps, they look more like milia. I would recommend you go see a board certified dermatologist for diagnosis and a treatment plan. Extraction and peels are a good option for treatment of these lesions.