Not to get sarcastic, but most men who tell their partners about old affairs are doing it to meet their own needs without a second thought about how it might affect their significant other. Yes, you may have a need to get it off your chest. In general, catharsis is good. In this particular case, tell your therapist. Getting it off your chest and onto your girlfriend's is likely to end the relationship.
Most relationships struggle with trying to recoup after an affair.
The pain, the breach of trust and the betrayal of loyalty are all quite destructive to the building of a long-term relationship. In general, so is hiding something and lack of communication. If you need help on this one, try counseling. It can never hurt to have some professional support behind you. Click on her picture for her bio.