Will I be able to get a resident card if I was convicted of crime?

I entered the U.S. with a tourist visa when I was 18 and stayed for 5 months then I came back and stayed in Texas for 5 months but the thrid time I visited the U.S. I never came back to my country (Mexico) and I have been here for the last 3 years. Little more than a year ago I was arrested for shoplifting and went to jail, they took my fingerprints and photos but I was released 2 days later without any citation to appear in court or bond required so I guess the grocery store dropped the charges against me. I have been with my girlfriend for the last 7 months and we want to get married and continue living in U.S. I went to the website of the county I was arrested (Fulton County in GA) and looked for my name but I couldn't find myself in the inmate search section. So far this arrest is the only problem I have gotten into and if is not for this my record would be totally clean even from driving violations. So my concern is about what are my chances that I can possibly not being in the jail system and if I'm how this can affect my possibilities of getting my permanent resident card? I have plenty of friends, most of them graduated from university that can testify I'm a decent person and I can tell that I committed that mistake while being in a very bad situation of almost a month without money, job, a house and being too proud to ask for help, but I don't know how much this information can help me.