It sounds like the document you were given may have been a humanitarian parole as a Honduran national so you could apply for TPS but this is all just speculation. If you were "paroled" into the country by US Border Patrol or USCBP, its a little white card, sometimes with you picture on it and a red entry stamp from them showing the date, port of entry and also the section of law for humanitarian parole then it would help you very much if you now get married to your boy friend who is a US citizen since he can then apply not only for your immigrant visa as his spouse but also apply for a green card here in the US since you were "paroled" into the U.S. (arguably if this is what you got). Parole is a legal fiction. It means you have no legal right to enter the US. You have no passport, no visa, no green card but the inspector at the border choses to exercise prosecutorial discretion and allows you to physically and legally enter the US in a lesser legal status, i.e. humanitarian parole for instance, or in the national benefit etc. So, although its difficult but perhaps we may be able to either ask the US Border Protection/USCBP to check their files and look for your record which is called a FOIA-Freedom of Information Act request, i.e. have them search their files for proof of your entry. This does take a long time usually up to a year. But in the meantime go ahead and get married to your U.S. citizen boy friend and apply for an immigrant visa as an immediate relative (spouse of a US citizen) while waiting for the FOIA result and once the proper proof is hopefully obtained then apply for your green card here in the U.S. with USCIS called "adjustment of status." You will need a competent immigration attorney to accomplish all of this. Good luck.
A CBP FOIA request may be necessary in your situation but I would also suggest consulting with competent immigration counsel before you proceed.
You can write to the government for proof of your entry papers and that you were inspected. If you marry your USC bf, you can be sponsored to get your greencard. Hire a lawyer to protect your legal rights.
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