Oxygen overdose in hospital

I was recently in hospital for minor surgery. I had a one night stay and the next morning when the nurse took my obs I was told I needed oxygen.

After half an hour of having oxygen blown up my nose I began to feel light headed as though I was going to faint. I called out to them & they rushed over to me - removed the oxygen pipes from my nose & took my blood pressure.

Then they just left me lying there & after half an hour I went back to feeling normal.

What I want to know is: Is it possible to be given an overdose of oxygen & if I had passed out with the oxygen still blowing up my nostrils what harm (if any) would it have done me?