Tyre clearance

I have just put a 28mm tire on my road bike (Giant OCR2). The wheel won't turn as the tire is now wedged tight by the caliper brake. It only needs a few mm.

I have tried the LBS & was told that I must go back to 23/25mm. I just wanted to tap the collective wisdom of the forum before I change again.

So my questions are;

1) Is there such a thing as a 'slim' road brake, that gives more clearance?
2) Does a brake with an offset mounting bolt & longer arms exist?

Tks in advance.