If I'm hypothyroid, can I still take Trileptal to control my pain?

Sure. I don't know of any specific problem with trileptal and thyroid status. Trileptal can decrease sodium levels and this should be checked by your doc. I often use trileptal for neuropathic pain sydromes like trigeminal neuralgia.
WHAT? (again) I know of no contraindication of taking trileptal with the existence of thyroid disease. My question would be why you are taking the trileptal for pain ?