Created a nice melody, struggling to work out chords that suit it.

I've watched as many videos as I can regarding working out chords for a melody.

They generally say to look at the root note of the melody and work out your scale, and that then opens up the chord options.

Problem is my melody doesn't seem to properly fit any scales.

I have a rolling D at the bottom (so the root I assume), but my top melody is primarly F# and A#, with the odd G and A for flavour.

I tried a few chord progressions based on the D major and minor scales, but they don't seem to gel with my melody, regardless of the pads/leads/arps I test.

Google says that D, F# and A# don't fall into any standard diatonic scale, and suggested changing my D to a D# for the F# Major scale, but D# sounds all wrong in the melody.

Any advice how to approach this?