Hi and welcome!
Is the blood sheer or is red-coloured (porphyine) urine?
If it is sheer blood, then the reproductive tract needs a closer look at. Sheer blood can come from an ovarian cyst having turned cancerous.
If you are seeing persistent red-coloured pees (which may or may not test high in blood) but there is no reaction to antibiotics and it is also not caused by a stone or bladder sludge irritating the bladder walls, then you are most likely dealing with a sterile (i.e. non-bacterial) interstitial (i.e. recurring) cystitis (bladder infection). This has become a lot more common over the last decade but is little known outside vet circles seeing plenty of piggies.
Sterile IC can usually only be diagnosed by default after all other urinary and reproductive tract problems have been excluded. It cannot be healed, only managed. Treatment is similar to SFC (sterile cat cystitis) with plenty of glucosamine and metacam. Glucosamine is classed as a food supplement and not as a medication but sterile IC seems to affect the natural glucosamine coating of the walls of the urinary tract that prevents the very corroding urine coming into contact with raw tissue.
We do recommend using a cat bladder supplement like Feliway cystease capsules (UK brand) or cystophan, which is widely available online, simply because it is very easy to dose. Just empty the contents of one capsule into 2ml of water, shake and wait until it has been absorbed. Shake again and either syringe 1 ml of the mix twice daily to give the 2 ml once every 24 hours; shake well before every use.
The severe form of sterile cavy IC can very newly also be treated with cartrofen injections (which is a very strong glucosamine based arthritis medication); this is only just being trialled by more open-minded UK vets after research abroad has shown that this also works for guinea pigs with sterile IC and not just cats. Feedback from the few forum members that have vets prepared to try this has been very positive. It is not cheap though! Please be aware that the glucosamine needs time to build up, so results are not instantly and can take several weeks to come through.
While sterile IC is not fatal and doesn't cause bladder stones in itself, it is also not something that goes away quickly. You are looking at years
rather than months until it very eventually goes away on its own after flaring up every few weeks or months, usually with the intervals lengthening as the IC is starting to fade in the latter stages.
You also want to review your diet, however, especially as your piggy has sludge (how badly? and is your vet doing something about it or not?). Most people are not aware that the bulk of the calcium in a piggy diet is coming from unfiltered water and from pellets; even pellets with no added calcium still contain more of it than the same weight of the veg highest in calcium. We strongly recommend to limit your pellets to 1 tablespoon per piggy per day max. You also want to review your veg diet; it is not about cutting all calcium out of the diet (that is as long term damaging as too much) but find a sustainable balance. Many piggies with sludge or bladder stones are not the best of drinkers, so you want to feed a bit more watery veg in order to encourage stronger pees once or twice daily. You cannot make a piggy drink more than they individually need, which varies enormously. You also have to be aware that when feeding more watery veg your piggy will drink less water; the individual fluid need is not getting more because you feed more.
With IC you want to ideally stick to a regular limited diet that mimics the diet they have evolved on as much as possible in an urban setting. Veg, especially not regularly fed one, can in some cases trigger cute symptoms, including grass when it is not a regular part of the diet in at last a small amount.
Please take the time to read our diet guide, which looks at diet as a whole as well as at all food groups in detail. It also has a chapter on dietary recommendations for guinea pigs with long term urinary tract issues with some additional tweaks to the normal general diet.
Here is the link:
Long Term Balanced General And Special Needs Guinea Pig Diets
Please do NOT apply sudocrem too much and too thickly because overuse dries the skin and can cause tiny cracks in the skin through which infection can enter. Just gently wipe the bum and the underside of the feet very regularly with a warm, damp plain water rag (bum bath) and change the bedding in the sleeping/favourite sitting areas once or twice daily.
The care tips for piggies with urine scald are essentially he same as for piggies with mobility issues (chapter 4); you can find them in this guide here:
Looking after guinea pigs with limited or no mobility
I hope that this helps you?