Send DWP a letter pointing out you made a mistake and send them the dates, they should have it on their records.
There are certain criteria to claiming both SDP and EDP, the first being you have to be in a receipt of a means tested benefit. You will not be eligible for SDP during the period your mother claimed CA or if you were not living on your own unless who you were living with was also in receipt of a qualifying benefit.
I would advise you to seek help from your local Welfare Rights Organisation who can help you apply for an 'anytime review'.
Gary
Nothing on this board constitutes legal advice - always consult a professional about specific problems