advertisement designer and a web designer is a big difference, when in college you are able to only major in one of the subjects.

You should square it down to one.

Usually in the Graphic Design course they have the following -

Multimedia
Graphic Design
Advertising
Illustration

If I were you I would encourage you do more extensive research and also realise that in this line its is very competitive and there is no going back once you start. Especially in advertising it is in a line where it is a very competitive field and a lot of budget is spend on adverts.

Btw you should read my blog regarding an issue of unemployed design students. I hope you get a better grasp of this particular matter.

Cheerios