Hi Pattie,
Thanks for your question.
Kitten suckling it is typically a juvenile behaviour that disappears with age. In fact, one of my cats used to do this with my wife but stopped promptly around the age of 4 months. It’s very possible they will grow out of it. If you want to be more proactive, I would simply discourage it by walking away from her when she starts doing it. I do not believe this will be damaging to your relationship. I’m more worried that you are becoming an outlet for a behavior which is not ideal and can worsen to the point of causing you harm if she learns that biting you is appropriate.
The fact that you are giving lysine means that someone is suspicious of the kittens having a herpes virus. The fact that you don’t mention herpes virus in your question, very likely means that it has not been definitively diagnosed. I’m almost certain that the right diagnostics have not been performed and you have yet to come to a diagnosis. There are many viral infections that can cause congestion and watery eyes in kittens. Some are commonly found in shelter environments. These are herpes virus, calicivirus, mycoplasma, chlamydia, feline immunodeficiency virus and feline leukaemia virus. I recommend you perform blood tests and an upper respiratory and ocular viral panel to determine the cause of these symptoms. You’ll also want to keep in mind that bacterial infections can occur secondary to viral infections, so antibiotic treatment may be necessary as well.
I hope this helps. Good luck!
Dr. Clayton Greenway