Precise erasing or deleting

Hi. 
I'm a complete newbie with about two weeks of Illustrator experience. I took a .jpg of a custom font that doesn't exist anywhere. And I'm making other letters in the same style of the custom font .jpg so it says something completely different. I'm completely done and I like how it looks, but I have some issues with transparency in a few small places. I've discovered that I can use the "erase" tool to erase the white color that is causing my transparency issues, however I can't do it accurately. Here's my question....it is extremely difficult to erase precisely, right up against the perfectly straight lines of each character in the font. Is there a way to use a different tool than the eraser to make very precise areas of transparency right up to each character?  Seems I should be able to use the pen tool to make precise guides of which areas I want to eliminate. 

Thanks.