I also think that it is very likely ringworm you are dealing with. You will need to treat the companion with an antifungal bath or dip, too, if you want to prevent an outbreak; the incubation period is 10-14 days before ringworm breaks out. Not all guinea pigs catch ringworm from their comrades, but you do not want to chance having to go through it all again. Ringworm spores (and there are thousands in an acute outbreak) can survive up to 18 months. Please be aware that ringworm is highly transmittable to other mammals (including humans!). It is the one thing that you can catch from your guinea pigs; strict hygiene and investing in some good quality antifungal disinfectants is key.
The currently most effective treatment is an oral systemic fungal; sporonox is the mildest of these with the smallest impact on the kidneys, especially with advanced ringworm like yours, as it will get everywhere that is difficult to reach or very sensitive to treat, like right next to the eyes. Please ask your vet whether he would consider it. It is now increasingly prescribed by piggy savvy vets and forum members (including myself) have made good experiences with it.
The good news is that as soon as the ringworm has cleared, the hair will grow back, usually in the order it has fallen out. With your little one should be covered in hair again within a month's time.
If your vet decides to also treat for mites, you have to be aware that there needs to be a gap of at least 48 hours between any topical treatments. Please never treat on spec and not to use any low-dosed pet shop product that are only geared towards the prevention, but not the treament of a skin issue.
Here are our tips:
https://www.theguineapigforum.co.uk/threads/ringworm-hygiene-and-pictures.115402/
here is more information on ringworm and anti-fungal products available in the US:
http://www.guinealynx.info/fungus.html
http://www.gorgeousguineas.com/photogallery.html
All the best! You are welcome to ask any questions at any time. We also have got lots of information for new owners at the top our various Care sections that may help you settle in your new piggies.