I have been having severe pain in both my hands and my feet.

I suspect we can assume you haven't sustained any trauma or injury recently since you didn't mention this.  Infections can cause pain in hands & feet but it's not likely to have infections in two separate places at the same time.  Blood clots can cause pain but again it's rare to have them in two separate areas.  Arthritis, both inflammatory and non-inflammatory, is the most common reason for hand & feet pain, that is localized to the joints.  It's possible that you're referring to muscle pain rather than joint pain (you didn't specify) which might be due to medication side effects.  Best to go see you family physician for a complete evaluation.  Good luck!