I used to be a permanent resident, but my green card expired in 2013. I filed form N-400, paid my fee, and was able to get an appointment for biometrics and a USCIS exam within that same year. On the day of my appointment, I was told by the officer that I was already a citizen; deriving US citizenship from my father (a US citizen) in accordance with section 320. I was told that I needed to file an N-600 to get a citizen certificate instead.
However, I never followed up on that. I've been holding off because that application would have cost me another fee. The problem is, now I need to travel to Mexico but I have no proof of my US citizenship. I have my expired permanent resident card and a paper that was given to me on the day of my appointment stating the withdrawal of my application since I was already a US citizen.
My question is: On re-entry to the US (Tijuana -> San Ysidro), would the border patrol people let me back into the US? Are they able to look up that I am a US citizen? I need to travel in the next 3 weeks, so it's kind of an emergency for me.