Poked inside of my nose by accident. Will it cause damage?

I'm sorry to hear about your incident. It depends if you had a septoplasty , then the internal damage could change the outcome. It also depends on how far out you are in regards to your surgery. You should contact your doctor for a follow up to be safe.

The nose is very sensitive after surgery. Just touching the nose too roughly may make it feel like it has rebroken. If you have any concerns you should always call your surgeon. If your nose looks the same as before you hit it then you are most likely fine. 

First of all, you should call your surgeon.  If you did not bleed, you may be ok.  Again, call your surgeon.  None of us know exactly what was done; your surgeon does.