Since your entry into the United States was legal if you were to marry in good faith to a USC then you should be able to apply for adjustment of status. I would however recommend you meet with any attorney to review your documents. My office is located in McKinney just north of Plano. If you wish to schedule a consult please contact my office or email a request. Good luck!
Since you are an lpr rather than a naturalized citizen then you don't have to file a separate I-130. but if you feel compelled to do something then you can amend the I-130 and provide the child's birth certificate or upon receiving the visa immigrant document from the national visa center you can inform them of the additional derivative beneficiary.
I agree with attorney Mulder retain counsel before filing. Your attorney can request a copy of your previous filings with a FOIA request. Whatever information was provided in those applications should not conflict with information you provide when applying now (for example date of entry) in addition you are not certain as to what occurred after your failure to appear to interview if your case got referred to the immigration court then you will need to start there.
Since you are in Denton I can recommend Sarah Roland who handles criminal cases of this nature and Micah Belden (from Sherman Tx) who have served as criminal counsel in cases where my clients required post conviction relief. I would encourage you to contact them.