Hi, new and need help with PIP please?

Hi all,

Long story short: 
I am 27 years old and have scoliosis, developmental dysplasia of the spine, ehlers danlos syndrome, and (supposedly) fibromyalgia. I cannot stand up straight for the first couple of hours of the day, I experience frequent subluxes of various joints, including my jaw, knees, toes, and fingers. I struggle to walk around a small shop without sitting down. Since 2016 my partner has not worked, as I am unable to do basic things for myself, and do not leave the house alone for fear of subluxing something and having a fall (which was the ultimate reason for him eventually giving up his job in 2016 as he was working 3 hours away when I had a fall outside out daughters nursery). 
I work as an Independent Research Consultant, and have slowly increased my hours since my OH gave up work to try to support us, until I am now working over 100 hours per week. This is all getting too much for me, so I was recently persuaded to apply for PIP. 
Went for PIP assessment, told her my main issues were not leaving the house without another person, needing help washing my hair (or anything with arms above head), needing supervision whilst eating (subluxing jaw every five seconds whilst chewing is an obvious choking hazard), to name a few.  
Two weeks later I have had my decision back - 0 points. 

The reasons given are that I am able to work (note it does not state 'from home', which is an important point since my job does not require me to go anywhere!) so therefore do not struggle with disability, and that I do not take pain medication, so therefore cannot be in pain (even though my conditions are chronic so I have voiced my reluctance to begin pain medication at the ripe old age of 27, and also pain medication would prevent me from feeling the warning signs that usually let me know I am about to sublux something, like those I have. Even experiencing in my hips recently which require me to lie on the floor to prevent them coming out of their sockets). 

Surely under the Disability Act and Equality Act they are required to support my ability to work? I have had no other choice!

The letter basically suggests that if I gave up work and started taking pain medication I would be eligible. 


Am I wrong in thinking I should appeal this?
I am at the point where I need to decide whether to start using a wheelchair so I don't have to miss out on my little girls' activities, days out, etc. And this has totally invalidated how much pain I put up with and how much I struggle everyday .