Trying to understand something

Hi all, was wondering if someone could help me with some information. I recently won my PIP Tribunal on the 9th of July after the claim began on the 20th of October 2017. My welfare rights officer tells me I have been awarded the standard rate in both of the categories but she doesn't agree with it but nevertheless is a result. I doubt we can fight it any further plus I'm frightened to because of how long this has gone on and how ill it has made me. 

This brings me onto the main bit. I was told I would now be able to claim a severe premium for ESA because I live alone and nobody is caring for me. What I would like to know is can I call them on Monday and claim it or do I need to wait until the DWP contact me saying they've accepted my PIP tribunal decision. I called them a few days after I won the tribunal and they told me that they had received the information. Can I claim the severe premium now or do I have to wait as I'm not sure and forgot to ask my welfare rights officer like an idiot and now I'm embarrassed to call her on Monday and ask. 

Also one last thing please, is it true that all the time between my claim beginning and now they will backdate all the money and pay it all to me? Including the premium from the beginning of my ESA claim date? 

Thank you so much for reading, if you can help I would appreciate it because I'm lost lol.

-Dolly