Do I have a negative canthal tilt? What can I do about it? (photo)

In general, the lateral cathus should be about 1 mm higher than the medial canthus. When it is lower, it does give the eye a "sad" appearance.
Although lateral canthoplasty/canthoplexy may give you an improve result, a subtle lower lid graft to fix the retraction will likely give you a better, long lasting result.
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Yes it appears you have negative canthal tilt with lower eyelid retraction. Lower eyelid retraction surgery with canthoplasty may be considered to create more upturned eye shape. See an expert.

A negative canthal tilt means that the lateral canthal angle is lower than the inner canthal angle. It is possible to surgically change this. That does not in anyway mean that you need to have lateral cantal surgery. The effect of changing the position of the lateral canthus is subtle. Really, it is not a cosmetic surgery. The main reason for adjusting the canthal angle is that it is the lateral anchor for the upper eyelids. If the upper eyelid needs to have a ptosis correction, it is helpful to correct the position of the lateral canthus at the time of the ptosis surgery. If you have concerns about your eyes, I recommend a very thoughtful, detailed consultation to determine how best to achieve your goals.