If you are the legitimate father of the baby, you cannot be forced to have anything to do with the child but you can be forced by the courts to pay maintenance until the child has become an adult if you refuse to pay voluntarily. I'm afraid the repercussions of your brief three minute fling will haunt you for a very long time. if the mother of the baby is as irresponsible as you seem to be, there's a possibility that the child might not be yours, in which case I would demand a DNA test before getting involved in any financial support negotiations.
I hope your steady girlfriend dumps you. If you can't be faithful to her now before you've even made a commitment to marriage, it doesn't say much for your moral values. Next time you get drunk, keep your trousers firmly zipped up.