Is there anyway to make my downturned eyes more upturned or almond shaped? (Photo)

Yes.  A small incision procedure with a suture can be done to gently pull the outer portion of the lower eyelid upward that can give a more upturned appearance.  These are routinely performed by oculoplastic surgeons, but other plastic surgeons are trained to do these procedures as well.  Seek someone with the proper credentials, local/national reputation, and great reviews and before and after pictures.  Dr. Richard Anderson is in Salt Lake City, and is one of the world's most accomplished oculoplastic surgeons.  Best regards.

Thank you for posting your photos.  I would recommend you have a full evaluation as you may also have ptosis or droopy eyelids as is commonly known. This problem might be adding to your tired look. The position of your lower lid can be altered laterally with a procedure known as a canthopexy/plasty. I would suggest you look for a plastic surgeon with oculoplastic training as advanced knowledge and training in eyelid surgery is needed to correct both problems. Good luck!