Creating a .GIF with a transparent/no background
I am currently making a game with a bald eagle, and I created a GIF with the bald eagle flying. When I made the frames for the GIF, I made the backgrounds of each frame transparent, and then saved them as a PNG file (which supports transparencies) However, when I used a website to turn the frames I made into a GIF, the GIF came with a white background, which I don't want. When I try to remove the background, it also removes the head of the eagle (which is a variant of white). It also leaves a dusty layer of white dots around the image frames as well.
How can I make a new GIF without a background or edit my current GIF (or the frames of the GIF) as to where it does not have a background at all? I cannot make the background a solid color because the GIF will be moving around the screen on top of different colors. I can't use photoshop or other adobe products (too expensive).
I would really appreciate some help! Thanks-