I hated being a lone parent, OP, if that helps. I had five kids, their dad started out he was going to take them all, then disappeared to the other end of the country and hardly saw them at all, never paid a penny. There were days when I contemplated strapping them all (aged between 2-9) into the car and driving us all into the nearest reservoir. There was no time, no sleep (one ADHD, one non-diagnosed but 'difficult') and they were, basically, feral.
At times I would quite cheerfully have given them, never mind to their father, but to any passing person who expressed an interest in having them. It was hell. But gradually, gradually, as they got older, started to occupy themselves more, had friends and I could get some sleep, it got easier. Four went off to university, they are all now very well employed and happy and I have a great relationship with them. Their dad - not so much, they see him when he can be bothered but his behaviour towards them is ...erratic, and he seems to see them as a way of making money somehow. He has still never paid back the CMS and is now retired.
You are tired, OP. And it is hard. But you know you wouldn't ever hand your child over, you just need a break. I'm not going to suggest what people suggested to me about 'having a weekend away' or anything because that's usually impractical, but if you can carve yourself just a few minutes out of each day to do something you truly enjoy - knit, read a book, have a swim, watch Loose Women - things will start to improve. They really will.