As you appealed within the prescribed time limit, your appeal should proceed in the normal way. You should however receive an acknowledgement of the appeal by letter from the DLA Unit to confirm receipt. As you sent the notice of appeal by recorded delivery, if you have not done so already, it would be worthwhile checking via the Royal Mail website to ascertain when the DLA Unit signed for your correspondence, with your notice of the intention to appeal?
Appeals can take some considerable time to process, so it may be a while before you hear from the Tribunals Service, at which point you will be sent a bundle of papers which will contain all the relevant documents, the DLA appeal submission to the tribunal and a TAS1 enquiry form which should be completed and returned within 14 days.
Nothing on this board constitutes legal advice - always consult a professional about specific problems