It sounds like you're having a really hard time.
Do you have any support, any one that could give you a short break? If not then online support groups/services might be helpful.
There are rarely simple solutions to why some babies are more difficult than others - it's often a complex mix of factors including personality.
I can certainly relate to the 'won't be put down' - I had one like this for a year, with the added bonus of a toddler clinging to my legs.
It did get better. Once they could move independently then the problem changed to clearing up the chaos they left in their wake. I still preferred that to the constant clinging.
In terms of weaning I think it is important to remember the 'under 1 it's just for fun' - please don't let food/feeding become a battleground, it will just make it more stressful for both of you - 5 minutes is probably long enough to try out a new food.
I think you need to go back to your GP, not for her, but for you because you need to talk about how you are feeling and see if they can offer any help.
Getting outside every day does help, it doesn't matter where - local park, shops, wherever you can walk to, the walking for you can be meditative and for her there are lots of things to distract her and stimulate her.