Want to get my teeth whitened, however my dentist basically told me it's impossible? (photo)

I want to get my teeth whitened however I have a white spot on three different teeth. Wouldn't be too bad however one of them is on my front tooth and so very noticeable. It is a lot brighter and whiter than the rest of my tooth. My dentist said the only way to get rid of it is to drill and then put a colour filling of my tooth colour. However then when I get my teeth whitened the filling will be the old colour of my teeth and if I do it after whitening, my teeth colour will change anyway.