issues with adding a stroke/outline to image

probably a super newbie question, but i'm working on a jersey logo for a baseball team and it needs a white outline to make it stand out on the red jersey. I thought it would be as easy as adding a white stroke to the image, but I was mistaken. I hoped that flattening the image would make it one solid shape and easy to outline, but that doesn't work either. when i add a stroke or do object>path>outline stroke, it outlines all the black lines inside the image in white instead of outlining the outside of the image. hopefully someone can help me understand where i'm going wrong. i'll attach a couple photos in case my explanation sucks!

thanks!