Can they press charges on me? How does this work? What can they do to try and press charges on me? How do they go about evidence finding or do they only press charges on the other woman?
If they have evidence of you smuggling drugs into a prison or even for just having them in your possession they can certainly press charges against you for doing so. When you were there on your visit, you must have seen signs hanging in the visiting area warning you of this as well as other actions you could be arrested for and the general rules of conduct when you're visiting an inmate.
If the only evidence they have is the word of someone in custody, I doubt they will press the issue any further, as it would be almost impossible to prove you did this without additional witnesses, or physical evidence. But they have every right to deny your future requests to visit an inmate.
Who was this "other woman"? Was it someone you were obviously with, like someone you traveled there with when you went to visit? Possibly your son's girlfriend or spouse?