You can sue anyone for anything. However, if he has no money or assets, it might cost you more to sue him than you will get in return. Plus, first in line for any settlement will be your insurance company that paid your medical bills THEN you.
If you initially indicated you did not want charges pursued, call the police back and advise them that you have changed your mind and that you would like them to forward the case for prosecution. However, depending on the sobriety of all involved, and the statements of any witnesses, it might be possible that the DA will not pursue the matter, or he may pursue charges against both of you.
The police ill probably not give YOU the other party's info, but the info can be gained via subpoena or discovery as part of a criminal defense or a lawsuit. Your attorney will know how to obtain that info.
- Carl