I don't recall enough material for this to be a novel, but I may have simply forgotten a great deal.
The protagonist (young, male, uninfected) is transporting an infected young woman to either a quarantine area or a safe zone. If I'm not conflating stories, this was set in the U.S. and he's headed roughly for Florida. I don't recall if he's doing this out of a sense of what's right, or because he's been recruited/paid to do it.
The infection causes people to grow novel sense organs, like the ability to taste things with their hands. (There may be further effects as the infection progresses, but that happens off-screen.)
They naturally become friendly, and one night he wakes up to find she's running her hands over his face - which will transmit the infection to him.
There are some (2?) scientists involved who are sympathetic/helpful; they offer to try to keep him from getting infected, which essentially involves an acid bath. He changes his mind at the last minute, deciding to accept being infected to stay with the young woman.
One of the scientists is infected, and in order to stay focused on his work he chooses to chemically burn off any sense organs that grow on him.
I feel like I read this about 12-15 years ago.