Bumps Under the Eyes? (photo)

Milia are tiny inclusion cysts. They are particularly common all over the face, including under the eyes. I have found that numerous milia can be easily and effectively treated via the use of a radiosurgery. For over twenty-five years I have used the Ellman Surgitron radiosurgical device fixed with a superfine needle probe to be excellent for this purpose. Following local anesthesia, short bursts of energy lasting only a fraction of second  are applied to the cysts effectively destroying them without any signficant damage to surrounding tissue. Tiny crusts form at the treatment site, which fall off in a few days. I have found the results of this approach to be quite gratifying. Consultation with a board certified plastic surgeon or cosmetic dermatologist is strongly recommended. 

Small white bumps of the lower lids are milia which are benign tiny keratin filled cysts.  Because there is no opening to the surface of the skin, they cannot be extracted unless the skin is nicked with a small needle or scalpel.  It is recommended that this be done by a professional.  To reduce the risk of recurrence, salicylic acid products, retinoids or retinols may be used.  Gentle exfoliation may be beneficial in prevention and also make extraction of existing milia easier but avoid harsh exfoliation since this may actually cause milia.  You may also need to change under eye moisturizers if the one you are using is too heavy and take sun precautions since there is some debate on whether sun exposure can be a causal factor.  

Lower lid bumps can be milia or xanthelasma. The photo doesn't clarify this. I recommend that you see a board certified plastic surgeon or dermatologist in consultation.