Why does drainage cause my gums to itch ?

Itching gums: I'm not sure what kind of drainage you're referring to. If it's throat or nasal or sinus drainage, it may be due to allergies, and allergies can cause itching of the gums. You might try rinsing your mouth with liquid benadryl, (diphenhydramine) which helps itching from allergic reactions. If this doesn't help, see a dentist for an evaluation.

Healing: Epithelial healing or migration over the surface may contribute to your itching feeling. Most watch for is the change in color from red to light pink, as the gum tissue becomes healthy. Keep on brushing and follow up with your dentist.