I have taken drug nimesil several times with alcohol when i had tooth pain, as i have heard combination nimesil with alcohol can cause serious liver injury, should i see doctor and check my liver?

Alcohol is a poison that never did anybody any good, ever, so stay away from it. It will destroy your brain cells, damage testicular cells that make testosterone, facilitate development of cancer in many organs, cause hepatitis, cirrhosis and pancreatitis etc. There is no safe level of alcohol intake. Quit while you are ahead. See a doctor if you have any concerns.

You should see your Dentist. Dental pain most often caused by infection. Nimasil (Alive) is an anti-inflammatory & analgesic, but will not cure infection. If you are a habitual/daily/binge/"medicinal" drinker, by all means see your Physician. If you want relief from oral infection(s), see your Dentist. A pain-killer with an alcohol chaser won't kill bacteria but can harm you.