Under eye skin texture - what is it and is it treatable? (Photo)

For about 4yrs I've had these tiny bumps under my eyes. My GP said that they are not milia and that they are basically genetic and nothing I can do. Is this true? I know it's not major compared to some skin issues but they really bother me. Also have loads of fine lines and the general texture is horrible. I don't feel they look like the eyes of a 24 year old! Would this require a cosmetic treatment at a plastic surgeon or something performed by a dermatologist? Thanks in advance :)

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