Are my eyes really at different heights, and if so, is there anything I can do? (Photo)

You do have a mild asymmery between the two eyes, and this is a result of asymmetry between the two eye sockets (orbit). This a very normal phenomenon. Nobody is perfectly symmetrical. Craniofacial Surgery to try to fix this is a massive undertaking and almost never done for something this subtle. I would recommend trying to put this behind you and not spending much more time worrying about this.

The amount of asymmetry in your eyelids is within normal limits, and eyelid surgery is not required. It is important understand that there are 2 halves of the face, and there never exactly symmetrical. The Nose can be straightened with a closed rhinoplasty approach which involves osteotomies placed in the nasal bones and a spreader graft placed underneath the concave upper lateral cartilage on your left side.