You have to start by separating different parts of the image into layers. If you don't have the original layered artwork you will have to rotoscope. This would be a start:
The next step would be to duplicate the layers you want to apply glow effects to, apply the effects, and control the visibility of the glow with masks and/or track mattes.
If you just throw a glow on the whole image then the different colors and edges will all react to the effect.
It sounds like you are new. I suggest you spend some time with the User Guide
The first one needs some kind of bright image to create te glow effect, the second one needs your object to have an alpha channel to create the glow on the outside of your graphic. You can also try to combine that with a transfer mode (Add) in the timeline panel.