After 2 MS exacerbations the back of my hands ache from below knuckles to wrist. Any tips outside of medications?

Neuro Rehab. Seek out a physical therapist who is good at neuro-rehabilitation. They may suggest appropriate exercises.
Sure. Recommend you see hand therapist or OT. Also, urge you to take a medication for MS. Your best bets include Tysabri (natalizumab) or Gilenya.
Topical analgesics. In ms, even a very minor sensory disturbance can be painful. Generally gabapentin, tramadol, carbamazepine, and duloxetine are helpful for painful neuropathic symptoms. However, topical anesthetics are often helpful. "icy hot" bengay, bluestar and other mentholatum or salicylate based products often help. So does 1% capsaicin, although care is needed in application. Tens units also can help.