Hiya! Tricky one here, but I appreciate anyone’s advice

I’m a full time student above A-level and applied for UC in September 2022. Me and my mum went in and she spoke on my behalf because I can’t talk and they couldn’t confirm my eligibility due to my education. An hour after my second appointment at the job centre, my claim was closed.
I was told that because I wasn’t assessed for work capability before my course started, I’m ineligible. I’ve applied for it again as my course is ending in less than a month which I was told by ESA is allowed.
I’m being told I’m not eligible despite giving them a fit note and being in receipt of PIP. I’m being rejected before I’m even assessed. It’s so aggravating because after I have the work capability assessment I can claim while in higher education. It’s so stressful as I’ll have no money over summer. I can’t work.
I appreciate any input from anyone. Thanks so much in advance.