I would be very skeptical of a surgeon who would offer you a surgery without personally examining you. To do get cookie cutter surgery. You will be harmed by this approach. Most eyelid surgeons are not trained to perform ptosis surgery. You need a careful personal assessment and based on that examination, the surgeon will be able to know precisely what surgery would be of benefit for you. Please be safe out there.
Thank you for sharing your case and photos. It is difficult to answer your questions without a consultation. The thickness you see under your eyes is the normal orbicularis oculi muscle that is larger in young people. This can be improved with surgery or filler injections. You should schedule a consultation with a board certified oculoplastic surgeon who has experience in both techniques. After a thorough discussion of your goals, the right treatment can be recommended. Good luck!