I have a website and need all white backgrounds. When I shoot a photo, even when the background is white, it will show up as gray in photoshop. When I try and use the paint can and clcik on the background to try and make all of the background white - what will happen 9 times out of 10 - is the subject I am shooting gets white streaks across it also. How can I just get the background to turn white and not the subject?

You should never ever use the Contrast/Brightness controls that are within Photoshop. Pros that use this application all the time know this and preach it consistently. What happen is that it dulls out other areas of your image. There's actually a few ways you can do this. 
If I saw exactly what you are doing I'd be able to help you better. But, for a quick solution.....you need to use selections in photoshop in almost 95% of the cases. But, you can change your tolerance setting lower for your magic wand tool until it only selects the grey pixels what should be white. Then fill them with white.
There's 5 other ways of doing this on a more professional level but don't know your skill level with Photoshop. You could use adjustment layers and apply a "Levels" or "Curve" to your image. Or get a selection from your channels and adjust from there.

Adjust the Contrast/Brightness will do the trick.

Let me know if you need further assistance.