Please have your boy seen as an emergency NOW!
The lethargy is most likely at least partly from him not eating enough. Keep in mind that over 80% of the daily food intake is hay with veg only maning about 10-15% of what he is normally eating, and you see the problem. See a vet asap as an emergency. A lethargic piggy is one in danger of dying.
Since he is struggling to swallow, you have to feed him very little but often. If he cannot get any food down, then he will have to be put to sleep. It is really as critical as that!
Guinea pigs can go downhill in a matter of hours or just a few days. You do not have the time to wait.
List Of Life And Death Out-of-hours Emergencies
Not Eating, Weight Loss Over 50g And The Importance Of Syringe Feeding Fibre
Switch from weighing weekly to weighing daily at the same time, like before you feed evening or morning veg. it is the only way you can monitor the overall food intake and manage any top up syringe feed. A guinea should eat about 60 ml in 24 hours just to stay alive and keep the guts from slowing down and eventually closing down. the more you get down him, the greater the survival chances, but you have to be very careful that your guinea pig has swallowed anything before you give more. Yours may need 1/10 of a small syringe full to try whether anything is going down at all.
Complete Syringe Feeding Guide
If your boy has problems swallowing (hence the water in the nose), then you need to see a vet ASAP.
Please make sure that he checks the crucial back teeth for overgrown premolars which can trap the tongue and prevent chewing and swallowing. He also needs to check the mouth for anything stuck between the teeth or oral thrush; swelling in the throat or a throat infection that is closing the throat can also be involved. Piggies can also lose the ability to swallow through a neurological problem; I have lost a younger piggy of mine that way last year.
Incisors are self-sharpening if the back teeth are working fine. If the edges are even and not slanted, jagged pointing inwards (i.e. overgrown), then you have to assume that the back teeth are working fine, too, and that the dental system is balanced. Your vet can remove the inevitable gunk in the mouth gently with a cotton bud to have a look at the back. Please ask him whether he has ever dealt with guinea pig before you let him do any burring.
Please see a vet ASAP if your piggy is unwell; in an emergency like yours, you need to see any vet, general or exotics as soon as possible at any time of the day for life-saving measures; you can always see a specialist once your boy is safe. Step in with life saving support feeding ASAP to keep your piggy going until you can see a vet and until your boy is well enough to eat the full amount by himself.
I am keeping my fingers VERY firmly crossed!