and also I-131 is not an option, as it's only for those who are outside of USA.
But the
USCIS page I linked to, under "Re-Parole", specifically says that I-131, options 1.e or 1.f, can be used for re-parole of people who are inside the US on parole:
Parole ends on the date the parole period expires, is revoked, or when the parolee leaves the United States or obtains an immigration status, whichever happens first. Although parole is temporary in nature, in some instances, an individual may need to remain in the United States beyond the period of authorized parole. In such instances, an individual may request re-parole from within the United States.
The petitioner may request re-parole by:
Filing a new Form I-131, Application for Travel Document;
Checking box 1.e or 1.f in Part 2 of the form; and
Writing “re-parole” across the top of the application.
Filing a new Form I-134, Declaration of Financial Support;
Including required fees (or request for fee waiver); and
Submitting materials and evidence to support re-parole, including an explanation and providing supporting documents on the need for an additional authorized parole period.
The Department of State manual,
9 FAM 202.3-2(B).d, also mentions that I-131 can be filed by people in the US on parole to seek re-parole:
Parolees generally must depart the United States before the end of the authorized parole period; however, some circumstances may permit an individual to remain in the United States beyond the authorized parole period. In such situations, an individual may request to be re-paroled by filing Form I-131, or the U.S. Government agency that made the original parole request may request an individual be re-paroled.
So it must be possible to file I-131 for extension of parole in at least some circumstances.
However, I am not sure it would apply to your circumstance, because you were granted humanitarian parole by CBP without approval from USCIS first, right? The USCIS
I-131 filing addresses page, under "Humanitarian Parole Applicants", includes "Inside the United States with parole previously authorized by USCIS from outside of the United States and requesting re-parole". But in your case, you were not previously authorized by USCIS, right? On the
CBP page I linked to, it says people whose parole was granted by CBP should contact the port of entry for an extension:
If a foreign national requires an extension of a parole granted by CBP, please contact the Port of Entry where the parole was granted.
So I think, in your case, you should contact CBP first.