If you were not caught by the cameras, then consider yourself lucky. People get fined for their mistakes as this acts as a deterrent.
Since, you were driving your father's car, the fine would appear under his name. There is nothing you can do about this. You are possibly trying to hide the incident from your father.
If the fine does appear under your father's name, just do the old man a favour by paying it by yourself. You can do this.
Possibly, you may get some spankings from your dad for your erratic behaviour, but then like the fine, it would correct you and you will be driving carefully in future.
Yes, you deserve to be spanked.