What a cutie! Try this product:

Viralys (L-Lysine) Oral Gel For Cats

I bought them on Amazon but just checked it out and they don't have them right now. But you can get them from local vet office. It is supplement so very safe. I got my cat from the shelter and he got the same symptoms with your baby and I took him to see the vet and got this supplement which worked great on my cat. Good luck!