PIP lower rate mobility not given

I received the letter yesterday saying I have got the standard rate PIP, thank goodness, gaining 11 points; but not the mobility component. I got 0 Points.
I received the report that the assessor made; and because I was having a relatively good day during the assessment, and not showing the gamut of my symptoms which are mental health and physical.
Physical Health: On my form and in the evidence it stated that I have variable days regarding my physical health which is Chronic Fatigue Syndrome. I cannot walk far at any time, and I always have a stick I use. If I actually feel well and I try to do more I have ‘post-exertion malaise’ which means I can end up in bed the next day as I feel so weak and in pain. This also includes having any stress emotionally and needing to speak or look at a screen too long. These can cause the same symptoms to happen and this post-exertion fatigue to happen.
The day after the assessment I was unable to get up and move. I was so ill again. The assessor stated she thought I could walk 200 metres. This is far too far for me to walk (and I stressed that on this day I was quite good). She asked me how far she thought I could walk and I said on that day I could walk down the corridor – maybe 25 feet and sit down in the reception and wait for my friend to bring the car to the door. She then drove me home to my door. I then had to make it up some stairs. Resting as I went. I had to lie down, but it was the next day I felt so dreadful and could not get up apart from very slowly to the toilet.
Mental Health: Despite getting 11 points of the standard PIP rate, I got none for the mobility despite suffering PTSD which means I get triggered especially from seeing any men. I was sexually abused as a young teenager and in relationships. When I am triggered, I dissociate and have no idea what happens to me. I am unsafe in such circumstances. I can also go into a panic attack. Therefore I need someone to accompany me when I go out. This person always has to be female, and I always have to see a female doctor; as I asked for a female assessor. None of this was taken into consideration.
Medication: because I take no prescriptive medication for pain the assessor did not take any pain I have into consideration, and as there is no medication that helps me with my CFS I do not take any. I have weaned myself off SSRI’s as this was suggested for this and depression. It worked for neither. I do take a medication for bipolar disorder.
Also as I take no medication for anxiety she thought I did not have this severely. I took diazepam but this is something that you get quite addicted to and no doctor will prescribe long term. I did try beta blockers but with these, I got dizzy and sometimes lost my balance as it lowers blood pressure too much for me. I now use breath control…but when in a panic attack I need someone to cue me out of this to breathe.
I see I can write for a reconsideration of a decision. Will, what I have written above be enough to get enough points for the standard rate mobility? I need this to help pay someone to accompany me anywhere; and also take into consideration the need for a car and to pay petrol, or for a cab, to go anywhere with them accompanying me, as public transport can be quite triggering too if I could walk to get it.
Thanks for any advice.

Thank you, Gordon, I re-read your reply to my post re not getting the Lower Mobility Rate for the PIP.
I still have not received any reply to my form/letter of Mandatory Reconsideration Request requesting. I received a text saying it was received on the 11th April and can take 6 weeks to hear from them.
I saw my doctor today, and asked her if I could have a letter regarding my mental health issues that would give me the points necessary to qualify for this lower mobility rate. She is happy to write this for me.
I have been informed it will cost me £50 for this letter. I expected it to cost; if not quite this much!
My question: Is it worth my while getting this letter and sending in? Could it allow for the re-consideration without me having to go through the process of physically attending an appeal meeting? Otherwise, am I better off waiting and getting the psychiatrist to write something for that. I am not seeing my psychiatrist unitl next month and if I want the assessor to make a decision from the info to hand rather than having to go to appeal I should probably be pro-active now and get the doctor to write a letter for early next week. What do you think?

Thank you for your questions, Gordon,
I respond below;
1. Doctor will take what information she has from past documentation from psychologists & psychiatrists, and put in her current view of my current conditions in a letter. She will ring me to ask if it is OK by reading it out to me and discussing with me before she makes a final copy for me to send to DWP. She is 100% behind me in getting this allowance.
2. Payment for the letter is a lot given my circumstances, but if it helps to re-instate my mobility allowance worth it.
3. The psychiatrist will probably write a letter without payment. She is part of the crisis team that has been taking care of me. But I don't see her for a month.
4. I will indeed carry onto appeal if my MR is not accepted.

I realise writing these answers to you I had best get my doctor to do up a letter/report supporting my claim as by the time I see my psychiatrist it will be over 10 weeks and I do want the letter to be in time for the DWP to have a more up to date view that I do need this mobility allowance. Hopefully, this will sway them and I won't need to go to an actual physical appeal.

Questions to you:
Do you know what the rate of people getting MR without going to appeal is?
And,
If MR is not accepted and I then need to appeal - how long is the wait before I will be seen?

Thanks, Gordon, appreciate your help