Badger have you cleansed his eyes to see if he has a foreign body in there? Maybe a hay piece? (Boiled, cooled salty water and gauze is ideal)
There are loads of things that do irritate guinea-pigs respiratory systems - dusty hay, sawdust, the detergent that you wash their bedding in for example.
Take them back to basics with their bedding. I don't use sawdust , just newspaper and hay to sleep in and soft barley straw round the sides of their Pighouse to insulate (but mine are adults and the straw is much softer than the hay)
They have soft bathmats indoors and hay in a trug, I use Ecover to wash their bedding.
I've noticed the hay has been really bad in the past couple of years. Dry, sometimes a bit coarse, thistles, (and the odd bird wing for good measure 
). I bought some lovely fresh smelling animal hay for my boys but GP1 unfortunately got a huge hay seed in his eye.
GP1 occasionaly gets a clear nose drip if he has fresh grass- we asked at his Rodentologist appointment . Some GPs do have a 'hayfever' , unfortunate for a grass eating animal but he doesn't have any ill effects from it.
The lethargy is a worry though, GPs are lazy blighters but not lethargic. How old are your guineas?
It might be that your guinea-pig doesn't want water. Does he drink it when you move the water bottle?
Where did you get your piggies from? If they had a vet before can you take them to the same vet ? It's difficult to find a guinea-pig vet, but hopefully you've got one near you.
My older boy is a bit middleaged now, he's going a bit 'old man' now - bit saggy, bit jowly, still eats tons, poohs loads.
When his brother was ill last year , the first thing I noticed was his eyes. They were sunken and weepy. He was very lethargic and sat in a little tucked in stance, just 'nodding' back and forth. And he felt all meh and lethargic when he was lifted. Usually he'd skip away and give us a runaround when we tried to catch him.
Our vet couldn't find anything definitive wrong with him (teeth, temperature, weight all checked) He had a hay piece in his eye that we removed with warm salt water (boiled) and non fluffy gauze.
He went downhill and died within 48 hours even with us syringing Critical Care into him.
Hopefully your pig will rally round, but do try the changing of your bedding.
It might be your pig is allergic to something. Possibly something he's not used to , having changed house.
If you can, pick up a sachet of Critical Care from your vet for emergencies for your GP First Aid box. (Or for non-eating GP emergencies, mashed up pellets)