Help needed for PIP MR

Hi, this is the first time I have posted.
I have osteo arthritis and anaemia - I was in hospital early in the year for very severe anaemia ad a blood transfusion but am still not well. The anaemia causes fatigue.
I was awarded standard rate for both sections with 8 points for each.
I got my decision latter a couple of weeks ago, and phoned DWP to speak to a case manager. He told me that If I didn't send in medical evidence, the decision was not likely to be changed.
This seems so unfair. The assessor got so many things wrong on the report, some that would not make any difference like she said I live in a two storey house, we never discussed it, she just assumed as I spoke about stairs, my house is actually four storey, I have three flights of stairs, one down to a cellar, I don't go down there as it is brick stairs and I am frightened of falling onto the stone floor at the bottom, I can't use the top floor either as it has no handrails to it. She said I wore trousers and bent to lift my trouser legs up to show her my swollen knees - I have osteo arthritis, I was wearing a skirt and pulled it up from above the knee. She missed off such a lot of what I had said, I had a friend with me as well who agrees the report is rubbish in places, so many spelling mistakes and wrong information.
She said I only take half the prescribed dose of painkillers, I didn't say that at all, I said I don't always remember to take all of my iron tablets as they have to fit in with certain foods and by the time I can take them, I forget. She didn't put that I use a tablet box, which lost me points for an aid, or that my friend told her that she often calls in on her way home from work to remind me and aslo helps with my arthritis exercises as my balance is not good.. I also struggle with preparing food, I use a perching stool to sit and prepare meals as I can't stand for long, by the time I have prepared and cooked it, I am often too tired to eat it because of the fatigue so I tend to have to eat out a lot in cafes. She put that it was because of pain that I didn't cook for myself and she thought with aids I should be able to. I suppose I could, using a microwave but I prefer fresh food, I don't like ready meals.
I told her that I was unable to wash my hair myself and have to go to the hairdressers as I cannot stand for long enough - I can't get in a bath and don't have a shower to sit in, I also can't wash my feet. She said she thought I could do it with aids - the case manager on the phone agreed that with more aids I should be able to do it. Maybe I could wash my feet with the long handled sponge I use to have a wash, but I could not bend my knees to dry them.
I said I have to use an illuminated magnifying glass to read small print, she didn't mention that, only that as I drive, read a book (I can only do that in natural light or with the magnifier) and use a computer (which I have to have turned to large font), I could read with no more aid than reading glasses. She said I was observed to pass her papers out of my handbag, which she also said I bent to pick up, I didn't, my friend was holding it and passed me the papers to give her. I didn't have to read the papers, one was my xray report which I knew what was on, and the other was a hand written addition which I had written so of course I could read it, I had written it. So I got no marks there.
For mobility, she said I was observed to walk 25 metres at the centre, 10 to the lift, standing for 30 secs in the lift, then 15 metres, what she didn't say was that we stopped whilst I had asked her for some water. I argued with the case manager that it was on the flat and a warm Summers day and I was having a good day at the time. I had told her that it was a good day.
On a bad day, of which there are far more than good days, I couldn't have done that, I told her I am in pain all the time, I struggle with slopes and kerbs. My left leg is so full of fluid, it moves to the back of my knee and locks the muscles causing my leg to drag as it won't bend even high enough to get up a kerb and I get pain down the front of the leg, She put on the report that there were no variables which doesn't take into account bad days at all.
In several places in the report she had put that I was walking with a walking stick, which the physios had given me, I was walkiing slowly and that she noted I had trouble with my balance. Yet she said I could walk unaided!!! This surely indicates that I could not walk safely (Balance), reliably, in a timely manner (she said I walked slow) and I certainly couldn't have done it repeatedly. That surely should have warrented the 12 points not 8? The case manager did say that he could see that the comments in the box underneath the score said I walked with a stick and that he could change that to 10 but it would not make any difference overall. That still would not be taking into account that I have balance issues and walk slowly which she didn't mention in the box but had said in several places elsewhere.

I don't know what to do. I don't want to risk losing the standard awards I have already but don't really want to ask the doctor for a letter as he doesn't see me that often to know how much I struggle.
What do you think please?

On the mobility
.

Thanks Gordon. I don't know how else I can show that I can't walk far. The criteria says you must be able to do it safely, reliably, repeatedly and in a timely manner. In other places in the report itself the assessor said that I walked with a walking stick given to me by the physios, that I walked slowly and that my balance appeared poor, yet she only mentioned the walking stick in comments for the descriptor, and then even ticked the box that said I walked without aids.
The GP has seen my x-ray report which lists the problems with my joints, has the DWP, I sent it in as evidence. The GP has only seen me walk the short distance into his surgery.

The case manager who sent the award letter said that they don't take into account slopes, kerbs, stairs, or weather etc. Yet it is well known that cold damp weather affects people with arthritis badly. All those things are to do with getting around. If you struggle with kerbs, it makes it difficult to walk along a street etc.
I just don't know how to show it any other way.

I gave long detailed extra information which I sent in with the original PIP form but that doesn't seem to have been taken into account.

The mobility requirements do not take into account difficult terrain or weather conditions. It is purely about walking on the flat.