How to make a transparent background from decal on particle texture?

I attempt to add in my own texture that I made from paint, but the background ends up showing with it and it makes it look the way I don't want it to be. I try getting the background transparent on drawing apps, but when I save it the white background still appears. I examine the decals that are applied for the texture on the particles inside the toolbox, however, I still don't comprehend it.

For instance:

https://gyazo.com/e1b265ed79ca3f1c2485979918627fc3?token=c6a6e4383d57be5a6fdd7459be0f9886

Mine is the one on the left, and one on the right is what I sort of aim for my particles to look like. I'm a total novice at this so...

I'm looking forward to your feedback and advice.