I'm having difficulties with severe cramping in my legs, feet and hands after exercise despite drinking plenty of water and taking potassium. What next?

Difficult problem. Muscle cramps can happen due to electrolyte imbalance from sweating due to exercise. It may be best to check your electrolytes including sodium potassium, magnesium and calcium levels. If you are taking any medications like diuretics, statins or alcohol, they can aggravate muscle cramps. You should seek medical advice if you have not found an easy solution. Taking quinine water (tonic water) mayhe.
Go see your doctor. Make a hypothesis, act upon it, then measure results. Repeat. In other words, now it's time to measure your potassium & other minerals in your body. Also beware that taking quinolones such as your Levaquin (levofloxacin) is associated w/tendonitis/tendonopathy. So don't make sudden movements which might lead to tendon rupture. Check out fda warning: http://goo.Gl/26ayoo.