In California, if the hit and run causes property damage, that would be a misdemeanor charge. If you caused injury or death, it can be a felony.
The misdemeanor charge has a maximum possible penalty of 6 months in jail and a fine of $1,000, and the odds of your doing any jail for this charge are zero unless you take it all the way to trial
For you to be convicted of a felony hit or run, there would have to be injuries or the death of the other party and you'd have to be aware that such injuries were likely to occur. The DA has the discretion to prosecute the felony as a misdemeanor.
You have a defense to the charge as either a misdemeanor or a felony, which is that you felt no more than a bump in the road and never even realized you'd been in an accident.
I'm not trying to minimize this. Nobody wants a criminal record. But no criminal lawyer will tell you to go and confess to a hit and run at this point. It cannot help you by undoing the fact that you failed to stop, but it will hurt.
Yes, they can arrest you if they have probable cause
to believe that you committed a hit and run, which means that the second you would go over to confess to what you did, you would be charged.
They may have evidence which will allow them to arrest you anyway, but you don't have to hand them proof of guilt on a platter.