ESA Carer Premium- Am I eligible?

I am in receipt of PIP and ESA including the Severe Disability Premium (SDP). I live with my grandmother who receives State Pension, Pension Credit Guarantee Credit with SDP, and Attendance Allowance. We care for each other as we have different conditions, and we have other family members who assist us both.

I never applied for Carers Allowance as iI assumed it would remove our SDPs. However, I was informed that if I applied for Carers Allowance for my gran caring for me, she'd be denied the claim but would have an "underlying entitlement" to Carers Allowance making her a carer, and her Pension Credit would be increased by £36 per week.

My gran has today received then letter telling her she cannot claim Carers Allowance but has underlying entitlement and that she should contact the Pensions Service because she may be entitled to extra money.

What I would like to know is whether I can do the same in reverse, i.e. I apply for Carers Allowance for the caring I do for my gran. Would, in a similar way, I would not be eligible for Carers Allowance but would have an underlying entitlement and therefore get a Carer Premium, or does it work differently for ESA than Pension Credit?

I"d really appreciate it if you could advise me on this. We've been looking after each other for years and never knew about the Carer Premium. I'd always assumed we'd lose the SDP so I never asked Citizens Advice or on here.

Thanks in advance,

ka