Max number of gifts
I currently have 10 gifts in my inventory and even after spinning 20+ Pokestops i didn't get any more!
So I was wondering: Is there a max number of gifts I can have in my inventory?
Yes, there is a limit to how many gifts you can hold in your inventory. Once you have reached this limit, you cannot obtain any more gifts until you send them to your friends.
Niantic Support
You can hold a maximum of 10 Gifts in your Bag at any given time.