So you had no monitors? How did you figure out the headphones were distorting?
Likely not. There are a lot of things to work out in mixing.
Good is all relative - its a veritable minefield of things to work out when it comes to buying monitors. If you have a small room, a lot of people buy small drivers (5" or 6") which means your low end extension is not very flat. If you buy bigger drivers, then you have more problems with bass resonance in a small room and you need treatment, and low monitoring levels, headphones for cross reference, and usually a frequency analyzer to be able to make things translate.
So you can spend $2k on a set of Focal 6s but then....?
But that's mostly an issue for panning and spatial placement. there are boxes which can add some cross-feed (real or effect).
Like this $$$: https://www.avshop.ca/recording-studio- ... b9dcd0f1f1
HTH