My understanding is that you married a US citizen. In this situation, you must have filed a I-130/I-485 package ("Petition for Alien Relative/Application to Adjust Status to Permanent Residence"). If you did it in person, you were entitled to receive Work Authorization on the same date and, consequently, you were eligible to apply and receive Social Security Number thereafter. Also, if you were to leave the US to go home, you must apply for Advance Parole - a permission (like a visa) allowing you to re-enter the United States while your Family-based petition is pending. You could have gotten the Advanced Parole the same day you filed I-130/I-485.
Also, at the day of filing you should have been given a date of your first INS interview (usually, 6-7 months after filing of the petition package). Afer the interview, if the INS officer finds your evidence of bona fide marriage satisfactory, you will receive a "conditional green card" with all rights and privileges of a "real" green card. The "conditional" status will be removed from your green card around 2-year anniversary of your filing through appropriate procedures.
If you have not done all the listed steps or for some reasons did not receive the above referenced documents, you should as soon as possible contact an immigration attorney who would help you to sort out your situation.
