See, Superfrenchie1, I think you are amazing. You are bringing up two young children on your own. You work and earn more than I ever did. You had the strength to walk away from your partner. You are financially independent with two healthy children and you are still young.
You have so much going for you.
Go to the doctors and get some ADs. Seriously. They will help you get some perspective and feel more positive. After a few weeks, you will begin to feel healthy enough to realise that changes can be made and your problems are not insurmountable. Attempting to deal with the huge list of what's wrong with your life when you feel down and anxious is a recipe for disaster. Go and see the doctors and get some medical help first and foremost.
Once equipped with ADs and a better serotonin level, you will be ready to tackle your list.
Firstly, so what if you live in a rented flat at the moment. That's right, AT THE MOMENT. You don't know if it's going to be forever. You may well earn more and find a different place in the future. You may meet someone else and find a bigger place. You have no idea what might happen. You do, however, have to open your mind to other possibilities. Blitz the fleas, and possibly get rid of the cat if you can bear to. That way, the landlord can come in and fix the broken stuff. Declutter - get rid of stuff, sell it on ebay, whatever needs to be done to tidy the place up. Bring in some fresh flowers. Make some changes to your surroundings, whatever can be done within time and budget.
Have you considered going on the Housing Register? You may be offered something more affordable and a nicer home for your children. It's not compulsory to take what you are offered. Can you move somewhere else?
You owe money. Lots of people owe money. I owe money. Don't panic. Have you been to CAB and got some advice on how to deal with debt collecters? They can offer you plenty of help in addressing the collectors. Don't run away from this. Write letters explaining you have no money or offering them enough to get off your back. It won't be forever and you can't give what you don't have. As long as you can afford to put a roof over your families head and feed them at the moment then you are winning.
Work - once you begin to make these changes and feel more in control and postive, then work will seem easier. You may start to enjoy it again.
You say you are disgusting, fat etc... Be kind to yourself. You have done an amazing thing leaving your ex and bringing up two children by yourself.
You have more important things in your life to deal with than worrying about extra weight and perfectly coiffed hair at the moment. A good wash, a smile and a night's sleep will suffice until you feel ready to tackle such things as weight.
Losing weight is bloody hard, but you have done harder things in your life. When you feel more in control of your life, maybe then if you feel the need you can consider making changes to your appearance.
Have a bash at doing these things slowly and one by one. Remember life can take some interesting twists and turns and we can never really truly predict what will happen next.
Oh, and tell your EX to fuck off, man up and start pulling his weight.