Claiming JSA help?

Hey guys,

So in August last year I left my job before some investigation was complete so on my record it says I left for personal reasons.

Not long after I had an injury (September), meant in Jan I claimed backdated ESA (Would of claimed it right away when I had my injury but several mistakes by hosp and benefit department prevented that)

The doctor was signing me off, they stopped giving me doctors notes at the end of Jan and my final DR's note ran out on 5th Feb.

How would I now go about putting in a JSA claim? would it be straightforward over the phone? Also would they backdate my money from the day my final doctors note run out?

I'm wondering since if they wont backdate that money I will be planning on claiming carers allowance for someone I look after

Thanks