Your eyes are attractive and you should not do anything to change them. Remember that every procedure has risks and sequelae and the benefit must be weighed against these.
It is very hard to get a handle on what exactly the problem is based on the photos. Ultherapy will not lead to a sinking in of the eyes (enophthalmos) or change eye shape. The photos show beautiful eyes before and after. However, to have your concerns fully addressed, you may want to have a few in person opinions. Good luck.
It is very difficult to tell much from your pictures. You look very young and I don't see a significant excess of skin or fat prolapse. So I think it best that you get a couple of opinions in person from reputable oculoplastic or facial plastic surgeons. Be sure you have a great understanding of what they are suggesting. Then perhaps come back to Real Self and let us know more about your situation.
It is very hard to tell much from these photos as they are blurred. However, there is no way that an Ulthera treatment can cause loss of fat around and behind the eyes. You may instead be experiencing normal aging changes in the fat which can result in puffiness or hollowing depending on your fat distribution. You can also develop laxity of the lateral tendon although can't see that in these photos. Get a couple of in person opinions to go over your concerns.