Hello, my name is***** and I have over 20 years of experience as a veterinarian. I'm sorry to hear that your kitty has a fever and elevated blood levels of bilirubin.
Bilirubin increases secondary to increased red blood cell breakage and pigments being released, liver disease with poor liver cell ability to clear the bilirubin from the blood, or a blocked bile duct so that bilirubin cannot be released into the intestine.
A fever points toward some sort of inflammation, usually due to infection (viral or bacterial).
I assume that your fellow has had a complete blood count and biochemistry profile.
What does his liver look like on radiographs or with an ultrasound?
Has he had a bile acids test?
While elevated liver enzymes can point toward liver disease as the liver fails it may be too sick to produce enzymes, and thus with a very sick liver we can see normal or even low enzyme levels. In that case the liver should appear smaller than usual or irregularly shaped indicating a mass taking up space where normal liver tissue should be. I would recommend a bile acids test to make sure liver function is truly normal.
If his liver is truly normal then we need to look at red blood cell numbers and evidence of red cell lysis.
In a young cat red blood cell lysis along with a fever can be indicative of a mycoplasma infection, which is a infection passed by fleas. Cats that are positive for immunosuppressive viruses like Feline Leukemia or Feline Immunodeficiency Virus are more likely to get sick from this. Some cats can harbor the infection and only get sick when stressed (as an immunosuppressive virus would cause).
Finally obstruction of the bile duct is a possible cause as well. This can be from bile sludging, (thick bile), gall stones or a parasite called a liver fluke (not common but more commonly seen in outdoor, strays that hunted for food
). Tumors can cause bile duct blockage but he would be young to see cancer.
I highly recommend testing your fellow for Feline Leukemia, Feline Immunodeficiency Virus and a Mycoplasma infection. If it hasn't been done yet an ultrasound of his liver can be very helpful. We can look at the architecture of his liver and collect aspirates, check his bile duct and evaluate the rest of his abdomen.
It would be prudent to get him on intravenous fluids and an antibiotic called Doxycycline just in case this is related to a Mycoplasma infection.
Best of luck with your fellow, please let me know if you have any further questions.