"If I need to contact work for other things such as being off ill I have to get either my sister or my mum to make the phone call for me on my behalf. "
No you need to set up an Email arrangement.
My DD has moderate LDs, it's best to be as independent as possible in the workplace.
It will increase your self esteem and confidence.
The Manager should be supporting you by asking what you have difficulty with. So communication seems to be the main thing, which can easily be overcome.
Is your Manager less sympathetic because your Sister is in work, yet has the same problems?
If so that needs to be bought out in the open.
TBH, the Care sector can't sustain ongoing sick leave, especially in private residential homes. The Manager will be being pushed for answers. So it isn't personal, she has got to keep the Staff levels to just what is needed, to keep the Staff bill down, but has to comply with company/legal policies.