If you want it to heal you need to rest it. But there are limits to that, too. You need to maintain the flexibility and the muscle strength so when the tendon does heal you won't immediately re-injure it, and you need to move the hand enough throughout the day to circulate blood and lymphatic fluid through the injured area.

The key is you must ABSOLUTELY refrain from the activities that caused it to begin with, and that aggravate it while it's healing. Have you had a fitting done on your bike? If so, go back to the fitter and explain the issues you're having. Has your PT/OT observed you going about your activities of daily living and tried to correct movement patterns that are aggravating your tendinitis?

Massage your hands and forearms with a spiky ball to release the trigger points that are locking the tendons short. Whenever you find a trigger point - a hard, very tender point - give it extra attention. It will hurt like !@#$%. Stretch after the massage. Do the exercises your PT gave you religiously, and when the strengthening exercises stop being challenging, make sure you ask for increased resistance, even if you're already back "within normal limits" as far as their charts go.

The same thing would be true of your feet. It's unlikely that you can't run at all... much more likely that you need to release trigger points in the feet and calves, strengthen your hips, and correct your form, your shoes, or probably both.

You might take a look at your nutrition also and examine whether that's making you more prone to tendinitis...