I would try to take care of it without using a “middleman”, and do it as soon as you can. Given the fact that there’s a flea infestation and the apartment sounds like a mess (the landlord might take that as an indication that you and your roommate aren’t even responsible enough to keep the place picked up), the landlord might fine you $100 and evict you too, maybe on the grounds of health/safety or property damage reasons. You have to tell your roommate that her cats are still her pets, and they require a lot of time, money, and attention, and she can’t keep absolving herself of all responsibility by pinning it on you, when she isn’t willing to dedicate herself to their care. Not to mention, I’m not sure how she expects someone with chronic fatigue to take care of two extremely sick cats and a flea-infested apartment when she can’t even do it herself.
I’m sure she’s really busy, and really stressed, and I’m sure you care about her a lot. But she went and got these cats herself, against your wishes, and it’s incredibly unreasonable of her to expect you to deal with the fallout of her own bad decision.