Jimmy Swaggart is just as human as everyone else, even though our spiritual leaders should be held to a different standard as the underlings. If a spiritual leader leads by example, having an extra-marital affair isn't the best way to go. Swaggart's admission was as if he was saying "do as I say, not as I do" rather than leading by example.
Jimmy Swaggart's "I Have Sinned" speech was offered to his family, members of his church community (and the general public) in response to claims that he was having sexual relations with prostitutes. While he did not provide any details or respond to specific questions it was clear and without question the "sin" he was acknowledging was his relationships with prostitutes.
Yes, I believe this speech was a confession to admitting to an affair. Even if he did have an affair though, it will not break peoples faith in him. He has influenced so many people through his preachings on television that nothing could break their belief in his ideas and teachings.
Yes, Jimmy Swaggart's "I have sinned" speech was a confession of guilt to an affair, because sinning implies doing something that is wrong or immoral. Swaggart was trying to admit to it without actually having to come out and say it. Swaggart admitted what he had to, and carefully chose his words. But yes, it was an admission.
It would appear that whoever asked this question does not actually know what a prostitute is. Jimmy Swaggart's "I have sinned" speech was his not so humble attempt to mitigate damage from being caught with a prostitute on multiple occasions. If you're paying for sex, it's a business transaction -- not an affair.