If one of the coils is wound the "wrong" way, you simply swap over the ends in your circuit.
It doesn't matter whether you wind the coil with turns going one way or the other. However if you have 2 coils they may need to be wound the same way or opposite ways. It's not at all uncommon to see advice which reads "If the circuit doesn't operate, swap over the leads to inductor X".
I can see you've tried burning off the enamel. It may be easier to scrape it off with a sharp craft knife or use some emery paper (fold it over, place it on the wire and pull it off the wire. Repeat until shiny.) After you've removed the insulating coating, tin the ends of the wire.