Hello, my name is***** and I have over 20 years of experience as a veterinarian.
I'm sorry to hear that your cats Mowgli and Mia are suddenly not getting along and I'd like to help.
I understand that they are not eating, and I suspect that is because they are too stressed and upset to relax and eat. Once they settle down a bit they should eat.
Cats in the wild don't normally live together. They compete for food, reproduction, and sleeping areas and often fight. In homes where the resources are endless they may learn to live in peace and sometimes actually enjoy company. When animals suddenly change their attitudes toward one another it means that something has changed. Either there is some sort of stress in their lives, resources (including time with you) are less or someone isn't feeling well.
So ideally both should have a thorough physical examination, urinalysis and bloodwork to make sure all is OK. Cats are very good at picking on the one who is weak in the group. It's also possible that one has an undiagnosed health problem which is making her/him the target of her/his housemate's attacks. Cats are very keen at picking up a change in body odor which can signify sickness.
Make sure their urine is checked for any signs of crystals or infection and cultured to make sure a subclinical low grade infection isn't part of the problem. Bloodwork to look for internal organ disease and hyperthyroidism is advisable too.
If all is OK physically then there may be an emotional or environmental stress that is causing them to argue.
It may be a change in the home environment (favorite person is gone more or has a different schedule), construction, new baby or other new people in the home, new pet. It may also be related to something going on outside. If one or both are stressed by a stray animal or wildlife outdoors they can take it out on each other. This is called displaced or redirected aggression. If you think it is related to something you can change do so, block doors and window access and play soft music or the TV when you aren't home or at night to block outside noise. You can also use a product called Feliway which is a synthetic version of a feline pheromone used to mark things as "home" or safe. This can be purchased at large pets stores or on line. It comes in diffusors, sprays or a collar form that has impregnated pheromones that they can have with them at all times.
You might also try using a product called Bach's Rescue Remedy. This is a homeopathic remedy that can calm them down enough to learn to live peacefully again. It is added to the food and/or water.
If those things aren't working for now I would keep your two separated. We need to give them both some peace while we get this sorted out. The more they fight the harder it will be to reintroduce the successfully even once they have calmed down.
I would recommend feeding them on either side of the door that separates them so they start to associate each other's smell with a positive (food). I would use the same brush on both so that their smells are familiar to one another. Rotate beds and toys between the two areas so that nothing becomes one kitty's only.
If they seem to settle a little perhaps you can try limited visitation after they have had several days to calm down, but only when you are home and can supervise to change or alter behavior. Make sure to have plenty of cat perches or condos and toys so each can have their own place to rest and things to play with so there isn't competition for resources. If either cat starts to stalk use an airhorn to startle her. An immediate negative consequence that is always present and not physical may be enough to help change behavior.
If these measures aren't enough you can discuss oral medications with your veterinarian as well such as fluoxetine or amitriptyline as calming agents to decrease the stress and aggression. These don't need to be forever, just until we can settle them down and they learn to live in peace again.
I do find that when cats that previously got along fine, and now things have changed, that either medically or socially there's been a shift. It can be difficult to figure out and fix but that's usually the only way to restore peace.
Best of luck with your kitties. Let me know if you have any further questions.