Well, yes you can go to your nearest SSA office on Monday be early since sometimes are crowded, go with your original EAD card and your passport. From the SSA website you can download the form to apply for a new SSN or at the office you can fill it out while you are in line. They will give you a receipt and then wait to get in the mail. There are some offices that make you wait to check with the USCIS database that you have authorization to work or let you go and then you must wait several weeks, that depends on the SSA office.
Good luck,