"Let me know if you need anything" never converts into anything. Specific, time-boxed asks do: "Could you sit with Mum on Thursday from 2 to 4? Here's the sheet, and I'll be back at 4 sharp." People are relieved to be given a bounded job they know they can do well.
In the UK, ask your GP for a carer's health check, contact your local council for a carer's assessment, and ask about Carer's Allowance and respite (short breaks) services. Charities such as Carers UK and Carers Trust run helplines. This page stores nothing and sends nothing.