Bamf's Congestion - Advice/Help?

DH and I (and our vet) are concerned about Bamf's congestion. He has been congested since we brought him home on June 6th, although he was perfectly fine at the breeder's! He sneezes regularly (a few times a day) and when he sleeps or breathes deeply after a bout of intense playing, you can hear his little whistley breath - another nickname we have for him is Whistlenose. When he sleeps, he snores really adorably, too. He has a little discharge from his eyes (very, very mild, dries into tiny boogers that he flicks off) and some discharge from his nose (mild again).

Anyway, with the way he breaths, we can all tell that he is congested. He has been on an L-lysine supplement (both kittens have) since shortly after we brought them home. They went through one round of antibiotics, and Pixel seems fine now (she sneezes occasionally). My vet does not want to put them through more antibiotics, because that will kill all the good bacteria in their bellies, and Bamf also had trouble with soft stool for a long time (it's firm now, yay!).

So, here is what I am asking:

Is there anything I can do to help with the congestion, IE to help treat the symptoms? In the bathroom with a steamy shower, herbal supplements, etc?

Should I be worried that he may have an allergy? If so, what should I do to find out if he does or does not?

Should I be worried that he may have Herpes virus? Should I have him tested?

Basically, are there any tests that I should ask the vet to perform? Should I have her take a culture of his snotnose and see if there are bacteria or viruses and if they respond to any antibiotics? Should I have him tested for Herpes and/or other diseases?

I don't want to ignore it. My little boy doesn't need to be a Whistlenose forever, just because I didn't care enough to figure it out!

Thanks everyone!

Can he get a xray to see if there is a reason for it?

Steaming in the bathroom (the kitty sauna) will help. If my cat's congestion gets really bad, I take eucalyptus oil and put a few drops on an old washcloth and place it near where she's sleeping/resting, but out of her reach. It helps open up the nasal passages, but is VERY toxic to cats, so you don't want him to be ingesting it. Also, start giving your kitty about 500 mg/day of Lysine to boost the immune system.

As far as tests, ask him to run the Feline URD PCR test to check for feline herpes, calci virus, and a few others that I can't remember off the top of my head.

Thanks for the replies. I will ask my vet about an x-ray and the URD PCR test.

Does anyone else have any replies or advice?

I hope they find out why it keeps happening.