When I relax my facial muscles, I appear to have brow and eyelid ptosis. Are there non-surgical solutions? (photos)

Thank you for your question and photograph. You certainly have brow ptosis which could be corrected with a brow lift or endoscopic brow lift. Nonsurgical options include Botox or Dysport in the glabella and crows feet areas which can give you a little medial and lateral brow lift for 3-4 months. Do not get neurotoxins injected into your forehead as your brows will drop further.
To elevate your eyelids, you can try Upneeq. It is a prescription drop that you put in your eyes and will elevate your upper eyelids for 5-6 hours. You can get 2-3 treatments out of each vile and there are 45 vials per box.