Issue with white dots when saving for web

Hello! This is my first forum post and I have a question about saving images for the web and the white dots that appear. I have made many gifs for my twitch channel and was recently drawing a Jokur emote for my friends stream. I tried saving the drawing as png and there are white dots surrounding the image making it just unbearable and not good to publish. Does anyone have a solution for this?

This is the image I am having issues with. I tried using some diffusion and that helped a little bit but I am don't know a surefire way to avoid the lines.