No, the drainage is supposed to happen the way it does. If it's redirected to somewhere in your head, it just sits and grows bacteria.
You can have nasal polyps removed if you have them. You may not. https://www.mayoclinic.org/diseases-conditions/nasal-polyps/symptoms-causes/syc-20351888 You should talk to a doctor about this and find out if you do.
The best way to avoid a runny nose is to avoid allergens. (Haha I know - I'm allergic to everything, I know this is sometimes not possible.) When you come in your house, leave your shoes by the door, so you don't track pollen through your house. Wash your hair before going to bed so you don't get pollen on your pillow. Get allergy covers for your pillow and mattress. If you haven't yet, see an allergist and get tested. Maybe it isn't just seasonal allergies, but a food, or dust or mold or something you are allergic to.
I change my pillows every 6 months or so - I don't care that they say they are washable or what not. After 6 months or so, I start getting more congestion and headaches, and when I get a new pillow, it helps.
Yes, it sucks that the only things we can do are work with the allergens and there's no way to stop it, but that is the best we can do.