What a difficult time you are having. And is it also during Diwali? Everything happens at once!

My piggies also get worried if new people are in our house - especially talking loud or singing/music but we have a covid 'lockdown' at the minute so nobody is going in anybody else's house right now.
It sounds like you so much want the best for your piggies. They will not understand why they are separated it is true, but this forum is not in favour of putting intact males in with fertile females for a few reasons - one is there will be babies which are tricky to look after and another is that it risks the life of the female to give birth even if quite young and more so if older because her pelvic bones have fused together... there might be more reasons but I am a new member and still learning myself. Sometimes people have two cages where the pigs can see and smell each other through the bars - or if they have a bigger enclosure they put barrier bars down the middle. It is not ideal for piggies who want to be together but they can have contact through the bars at least.
In the UK people sometimes make mistakes - starting out with 2 piggies bought for their children, and ending up with
lots because the babies become fertile very young (3 weeks or less for little boys!) and you cannot always tell boy from girl when babies. People find they cannot cope, then we end up with lots of sad, unwanted piggies in rescue centres. The females can often be paired up but it is more tricky with the males. In many pet rescue centres in the UK it is standard practice to neuter (sterilise) the males who are single so they can be bonded with females for adoption in pairs... but there are many lonely males out there (my own George was one of them). The females are not sterilised (spayed) as standard - only if they have health problems due to the reproductive parts because it is a bigger operation. I am actually quite surprised your female has not been pregnant already but perhaps it is something related to the cysts which is affecting her hormones and causing infertility. Cysts on the ovaries are different types - some are harmless but some cause problems. Cysts in the uterus I have not heard of... but I am not a vet. My friend's female pig had an infection in the uterus and had to be spayed - she was worried for her poor girl in the operation but it went well and her girl got better and had a long life. I hope they can find some good treatment for your girl to make her better. Different antibiotics are used in different countries - over here they have to be prescribed by a vet so we cannot just buy them in a shop. Even antibiotic cream needs a prescription.
Your immediate problem is the not eating which is very important to get over quickly. Hay is most important because it keeps the guts moving and wears down the teeth. Antibiotics can sometimes affect appetite but your male is not on antibiotics is he(?) unless I missed something. Perhaps if you put the food near the bars where the pigs can eat together on each side it might encourage them because they will be used to eating together. If you end up having to feed mushed pellets by hand or syringe for a short time it is a new skill to learn but not so hard (there are guides on this site). Then there is the poor girl's cyst/infection problem to deal with at the vet. It is good to get a vet with experience in guinea-pigs but I understand this is not always possible and we can all only try our best. Once everyone is well and happy you could maybe think about sterilising one pig so they can go back in together but this is some way off... for now just make sure they are eating, comfortable, and in contact with each other through the barrier so they cannot mate. Your male will be stressed that some other male might appear to get his female so he will be more settled if he can see they are close together and there is no other male.
I will be thinking about you. It is such a worry when our pigs are unwell and we are trying to make all these decisions and do the right things. I wish you lots of luck ❤