I get that your not depressed ,people have a knee jerk reaction and cant see what they cant fix with pills.
Do you have another adult you can get help from? Lonliness is a practical prob as well as an emotional one. you arent broken you just need some practical solutions, your not broken, your just stuck.
If your house is such a tip ,limit the rooms kids are allowed into. Start with your bedroom and work from there.
Make it clutter free, fly lady it if you have to. You have laid down one rule and WHEN you kids see you respecting that space , keep that going and move onto the bathroom,then the kitchen...
Dont try to do everything and get discouraged, get the satisfaction from one job. Dont know how old your kids are, dont tell them to do things,keep them away from things you value (bedroom)and get them to work alomg side you (10 mins tidying kitchenfor example).
You cant do anything by yourself ,and you are not a failure for not being able to do this. You need an injection of adult help. How often do you get out of the house? If you are sitting in it ,you will feel like you are stewing (i know that).
I am chronically lonely, so this is do as I say not what I do right? Get involved with a social church(perk of being religeous),local volunteer society,help out at a food bank. Anything that developes a social life that you dont have to pay for and wont make you feel bad.
Help other people,and try to get your kids involved might help them turn around.Hope other peolpe have some ideas.Good luck