India is known to have highest rate of suicide, for having an unhealthy sex act you want to commit suice? Shame on you. Your parents took care of you when you were a toddler, spend so much on you and for a sick sex act you want to make them feel ashamed?
Accident happens in our life, people who can repent, take a lesson, and never repeats, thats the spirit. It would have been better to think with your head instead of dick head before the act, but once gone, its gone. Its time to forget and move on in life.
Seems you are too much affected by this that there is a change in your daily chores. Your girlfriend is sharp enough to see the change. Its not wise to speak to her and ask for pardon, rather we should sometimes learn to know how to hide truth for betterment. Tell her you were down for something related to money, like you lent to someone, never got back and was upset because the guy was too much trusted.
On the child part, why bother so much? If it was that old lady's ovulation period or not, if she is using contraceptive, you never know. If you have a doubt, go for a sperm count check up. Be sure of yourself.
My suggestion is, get over this, tell some logical lie and get back with your girlfriend, if she in not ex already. And never ever repeat the same mistake of messing up within family members.