Man, sounds like you're really going through it.
I totally understand your concerns around career progression, but I think it would be worth seeing the doc to talk about this. Even getting some meds on a short-term basis could potentially help you get through this without needing time away from work, yet even if it doesn't, there's no shame in being signed off for a week or two with stress or depression. Often, just taking that first step towards breaking the cycle off feeling shit can lift a whole load of weight from your shoulders.
Having a mental wellbeing problem is no different to having a physical wellbeing problem - I know many people still hold the contrary view, but in the same way that no-one would expect you to carry on as you would usually with a broken arm, nor should you be expected to when you're struggling with anxiety and / or depression.
Whatever you end up doing, I really hope things begin to lift for you much sooner rather than later. I can empathise with everything you've mentioned above, I've been through it myself on many occasions.
And take time out to be kind to yourself as well, try and be a bit selfish over the weekend and indulge yourself in something you really love.
Take it easy.