What can I do about the loose skin around my eyes?

Peel, laser, surgery. Depending on the severity and cause of the "loose skin" appearance (can be fat, fluid, or loss of skin tone and elasticity associated with aging, weight loss, illness, or hormone changes), a number of options can be considered, along with their pros, cons, and risk/benefit ratios. See an abps-certified plastic surgeon, not a doctor certified in areas unrelated to plastic surgery or by bogus boards.
Surgery. Surgery is an option, but the fractional laser is my favorite way to tighten loose skin around the eyes and even give the eyes a little lift.
Options. Some topical treatments can improve your skin there. Botox, fillers, prp therapy and fat transfer may also be appropriate. Chemical peels, laser resurfacing and surgical blepharoplasty are the definitive treatments. See an experienced plastic surgeon to help guide you in your decision. Be well.