Here's the problem - over the internet, unforunately, even the most experienced people may not be able to figure out what's wrong. When my piggy had flakes, I took her to the vet to figure it out.
The other problem is that you say you would rehome her if she was suffering. Generally, when guinea pigs get sick, you have MAYBE 24 hours (I belive it can be even less than that) to get them to the vet before it's too late. There have been two times with my girl where bloat happened in the middle of the night (1 am and 6 am). I literaly ahd to drop everything, get a cab, and go to the 24-hour emergency vet. Then, I had to stay there with her most of the night, and then we needed to do a follow-up exotic vet visit in the morning. Do you truly believe your parents would do that, if necessary? You don't have to answer it here - it's just something to consider. And the costs are expensive - we are talking hundreds, thousands of dollars (especially with conditions like, let's say, bladder stones, which can require multiple surgeries - and this is something very common). My girl is actually another good example. She has digestive issues that we can't diagnose. Every day is not an emergency, but she has required multiple vet visits, diagnostics, and meds, all VERY expensive - this had to be done, even though she was not on the verge of dying every time.
My other piggy has arthritis. So far, knock on wood, we are OK with just supplements, but she may need some medication in the future. Even to diagnose this, she required an x-ray. Again, this is not life-threatening, but it requries a vet.
And once the pig is already sick, rehoming her in time to get care would be extremely difficult. I know I have to do what it takes for my girls, but it's a huge financial and emotional responsibility, and it's hard - I love piggies, but I wouldn't take in an already sick pig in critical condition, because I simply don't have the resources to do that.
Again, I know it's hard. I know it's heartbreaking, actually. I would probably have the same reaction as you. But you are right, these medical issues do need to be caught early (and the older your pig gets the more likely the chance that something pops up - in fact, my vet said that my older girl should have bi-annual check-ups from now on, just to monitor arthritis and any potential reproductive issues), and if your parents are unwilling to do that, she needs another home.
Maybe you can adopt to someone who would let you visit once in a while or send you emails about her?
I think you will make a GREAT piggy caretaker, but just wait until you have your own money! That way, no one can stop you from doing what you need. Also, on your other posts, you mention getting another piggy. Please DEFINITELY don't do that if your parents won't even take the one to the vet.