Hi!
I am extremely sorry but your boy should see a vet as soon as possible for a respiratory tract infection, which can only be healed by an antibiotic as it is a bacterial infection. An un- or undertreated respiratory infection can kill or permanently damage.
Do you mean a ring of yellowish/greenish gunk around the eye? This is typical for a well developed upper respiratory infection.
If you have your boy less than a month (US)/ 2-3 weeks (UK), then you can reclaim the cost from your pet shop as exposure and infection have happened there.
More information on your customer rights and on URI (upper respiratory tract infection) in this guide here:
What to check and look out for in new guinea pigs (vet checks, sexing, parasites&illness)
Here are our bridging care tips. Please note that there are simply there to keep your guinea pig alive as best as you can until you can see a vet and have the appropriate treatment kicking in.
Please also be aware that the need to breathe comes before the need to drink and only thirdly the need to eat. This means that guinea pigs with URI are at high risk of losing weight very quicky and their guts closing down if they stop eating.
You need to step in with offering syringe feed and water promptly and monitor the weight daily on your kitchen scales. Keep in mind that veg and pellets should only make about 15% of the daily food intake while the mainstay is hay (over 80%), so you can actually miss this totally of you only look at your piggy nibbling on a little bit veg!
If your piggy is suddenly very lethargic, then it needs vet care asap to save its life.
Emergency, Crisis and Bridging Care until a Vet Appointment
How To Pick Up And Weigh Your Guinea Pig Safely
Please always include saving up for vet fees as part of the weekly living cost for any pet. Vet cost will make the life long largest budget post. Healthy guinea pigs have an average life span of 5-7 years, but they can live longer. They feel and suffer just as much as we or any larger pet.