Is it wrong that I can't go to the bathroom without picking my nose?
Were you taught that it is polite to go to the bathroom before picking your nose?
Yes, my parents and teachers always taught me and my siblings to go and pick our noses in private.
It's fine to want to pick your nose sometimes, but make sure that you don't do it when other people are around, because it can be disgusting for them.  If this is becoming a compulsion for you, though, you might want to ask a professional if they can help.
I might just do that if I can't stop.
Just keep doing what you are doing and it will be okay. Doing it in private is the right thing to do.