The white discharge might be a symptom but it might also be the normal fluid they produce to clean themselves. You sometimes see a white drop like a milky tear in the corner of one eye. Sometimes after a big sneeze I've also seen a little on the nose of one of my pigs (a black one - it shows up!) But I've never seen any white discharge from the mouth. Although guinea pigs can get oral thrush the symptoms are usually things like stopping eating and pink gums rather than the white discharge and crustiness humans with the same condition might show. There's no reason to think it's that. White from the mouth could reflect piggy not swallowing the saliva they naturally produce. This is the only thing I can think of here.
A little note about the gasX which I
think has the active ingredient simethicone(?) Simethicone works in babies by gathering all the gas together into a big bubble so baby can burp it up. But piggies don't burp - any gas has to pass through the back end. They have a very long thin gut for processing lots and lots of fibre (unlike humans who have a different gut made for eating many different food types). So forming a big bubble can actually make it more difficult for piggy to pass the gas which can make them uncomfortable. We have a product in the UK called Gripe Water which is sometimes used in cases of mild bloat - but if your girl is still eating and pooping it sounds like gas blocking the gut just isn't an issue for her. It's important to weigh poorly pigs every day at the same time to check they are maintaining their weight. There will be ups and downs (about 30g either way is quite normal) but you do not want to see day-on-day losses. This is where the support feeding comes in.
If she can walk properly sometimes but is then staggering and falling over it might not be a 'back-legs' issue - it could be weakness from being unwell more generally. Especially if there are other symptoms to suggest she is not feeling herself - and especially if you have another piggy getting ill at the same time when they have both been in good health previously.
So you have 2? Or more? And they are kept either together or next to each other? We need to consider either something infectious or something in the environment has changed: perhaps that they have both been fed something they shouldn't have.
Sometimes people feed a new type of veggie to a pig that they shouldn't - thinking that they can eat anything green. But there are quite a few things that are poisonous to piggies and can make them unwell. For instance, pigs sometimes enjoy the occasional tomato but should
never be given the green stalks/leaves of tomatoes (or potatoes) which are highly toxic. There are some houseplants that pigs will eat if they are given the chance but which are toxic too. My friend went to pick dandelion leaves for her pigs (a popular treat) but unfortunately took them from a roadside where dogs were taken to pee a lot - her poor pigs were very unwell for some time but they did survive. Both traffic residue and dog pee are toxic for piggies. Sometimes a bag of 'fresh hay' has somehow got water in which allows mould and fungus to grow. The bag will smell funny - like mushrooms perhaps. This is no good for pigs. So check with your mum whether anything new or unusual has been eaten by them. Whether any small children have come round to visit and perhaps might have fed something to the piggies.
But if your girl had a higher temperature that does suggest infection. Most of my personal experience is with urinary tract infections which don't tend to spread - one pig might get one but the others don't catch it. Pigs can get infections of the upper respiratory tract (lungs, basically) which are serious. They do not 'catch a cold' like people do so sometimes symptoms such as runny nose, crusty eyes, sneezing etc. are ignored thinking it's just a cold and it will go away. unfortunately with piggies this is not usually the case. Here is a link about URI with lists of symptoms
Guinea Lynx :: URI but basically they can be very hard to spot. Even looking at the breathing rate of piggies isn't much of a guide - you would expect breathing to be more quick and shallow but even the
normal breathing rate of these nervous little critters varies wildly. 80 bpm is an average but one of my pigs - completely healthy - had a bpm of 120. He was just a nervous little guy. URI will definitely need veterinary treatment. The vet has to listen for lung sounds with a stethoscope to see if they can hear fluid in there. Antibiotics (which are suitable for piggies) will be needed. There is a painkiller/anti-inflammatory called meloxicam which can also be used in piggies if they can get it (it's manufactured for dogs and cats).
One final note - some pigs take antibiotics with no problems. But sometimes a pig gets an antibiotic and although it treats their infection it also completely kills their appetite. The effect can be very dramatic. This is why we never treat pigs with antibiotics unless we have to - in the UK we need a vet prescription for any antibiotic at all - even antibiotic eye cream. Piggy must then be syringed and tempted to eat throughout the day to see him through until the course is finished. We had this battle with my old boy who needed weeks of treatment for a very stubborn infection and it put him right off his food. He lost a lot of weight (even when it didn't hurt him to pee any more - pain had stopped him eating at first) As soon as the AB course was completed he picked up his appetite again as it was before. He's a lot thinner but there was no alternative. I hope you can get some answers when you get back home. You sound like you love your pigs very much
I'm so sorry you are facing this situation x