I am not licensed to practice in Tennessee, so I will answer based on general principles of law.
What you are asking about is called palimony (instead of alimony). It would be helpful to have a lot more facts here about the nature of your relationship, but I see a couple of hurdles you would need to overcome. The first is one of co-habitation. Generally palimony suits occurr between people who lived together in a way that mirrored a marriage but simply were not married. That would not appear to be the case with you.
Though laws differ in each state, presented here are some general key factors that might play into the court's decision to award or deny a palimony settlement:
Longevity of the relationship.
An implied understanding between partners that one would financially provide for the other for the rest of his or her life.
Spoken promises between partners that can be substantiated or corroborated. Written financial agreements, if any exist.
Ability for the plaintiff to support himself or herself.
Sacrifices made by one partner to support the other by way of giving up a career path to take care of the home or children.
Sacrifices made by one partner to put the other partner through school so that he or she could earn a professional degree.
Disparity between incomes
As simply the other woman, I think you would have a difficult case because you did not live together and were aware of his wife. Still, a court might be receptive based on the precise nature of your relationhsip.
I would talk with a PA attorney.
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