Is there a substitute for lyrica (pregabalin) that will treat my pain but not cause weight gain?

Depends on the case: Lyrica (pregabalin) is a great anti-neuropathic medicine. The weight gain is usually water retention as opposed to gaining fat. There are a number of other agents which may be helpful. Topamax typically does not cause weight gain. This should be determined by the treating physician.

Adverse effect: Neurontin is the most likely "substitute". It to has the adverse effect of weight gain. Topamax (topiramate) would be a good option.