Hi,
Unfortunately with anxiety it's a viscious cycle when you have lack of sleep. I have suffered from anxiety since childhood and in the last few years, it has got worse and worse (no doubt due to menopause) and some days I just wish it would 'p' off...in fact, that's what you're meant to say to your anxiety...tell it to 'F'' off!
I find that if I have lack of sleep, my anxiety is worse so when I have a sleepless night and can't fall asleep and everything is going round and around in my mind I start to panic even more as I know my anxiety will be worse with lack of sleep.
I don't have many solutions to offer you other than I try to never let the anxiety beat me. I only work part time but on the days I have to work, I spend most of the morning imagining in my mind phoning my boss with some excuse or other not to go into work but when I make the effort and go, it does give me a boost. I feel I'm saying to my anxiety 'ha, you didn't beat me'.
I have never had medication or CBT for my anxiety but as it has worsened during menopause, I am wondering whether to ask my Dr for something but I use the website 'no more panic' which is really helpful but there are lots of different opinions on there about whether medication is the correct route. I would suggest you look on the website though as there are lots of helpful tips to combat anxiety and insomnia.
Good luck..