A coworker of mine just had new tires mounted on his truck. As soon as he left the shop he said he had symptoms similar to yours...humming noise with higher pitch at higher speeds. He went back to the tire shop and discovered that they mounted one of his directional tires backwards.
Since you just had a tire removed from the rim for a patch, you might want to check to make sure they mounted it the right way.
2010 RRSS Autobiography - #7 resonator delete
2008 335xi Coupe - sold