Hi Bonnie,
Legally there is nothing that prevents someone claiming both Carer’s Allowance and PIP at the same time. However, I always urge caution. Given that PIP is largely based on help required to do certain important day to day personal care tasks, if you claim CA then DWP may well take the view how can you look after another when you can't look after yourself? Of course it may depend the sort of caring you give compared with the personal care needs you actually have. It can work, but please think very carefully.
LL26
Nothing on this board constitutes legal advice - always consult a professional about specific problems 
