What can I do after publication with double affiliation in an open access journal?
There is nothing wrong with publishing a dual-affiliation paper. It happens often when a person conducts a piece of research at one institution but finishes writing it up at another institution. This is a genuine dual affiliation because writing is part of the scientific work.
That said, however, I am extremely suspicious of a journal that does not allow you to declare your own affiliation. Your description of that and other interactions leads me to question whether you are being scammed by a predatory publisher.  I would strongly recommend evaluating the quality of the publication and making sure you actually want to publish with them.