I would definitely quarantine a newbie. I didn't do it ONE time and... well, what is done is done.
Not sure of Watson's EXACT issues, but....do you have any interest in Lysine?
To quote someone else.. Lysine is needed for "growth, tissue repair, and the production of antibodies, horomones and enzymes." It also mentions that "if you're often tired, unable to concentrate, prone to bloodshot eyes, nausea, dizziness, hair loss, and anemia, you could have a lysine deficiency."
It may not help, but I don't believe it will hurt... if Watson is sharing an URI and/or kitty cold. Can you ask your vet? I'd be happy to send you some.