Yes, it appears you've unfortunately misunderstood the particulars of the requirement: the flights have to be operated by United or United Express, not necessarily purchased through the United web site, and codeshare flights do not count for the requirement. You must have stepped food on an airplane that says "United" on the outside for the flight to contribute toward the 4-segment minimum.

The only good news is that despite the difficulties you might have getting to the US, you do still have some time to accomplish that before the end of the year, if an opportunity arises for you. Moreover, flying internationally on United airplanes normally counts. Toward that end, if you do book additional flights and they are in Basic Economy, you should verify that they will count, as I seem to recall there's some nuances with regard to BE, segments, and premier qualifications.