'These new shoes are killing me' is a very common expression.

Andy and Gary's options are both good. You could also say "New shoes chafe my feet." http://dictionary.reference.com/browse/chafe

'Hurt' is the word that fits the gap. Also 'blister' might be correct if the sore is in fact a blister. Andy's phrase is a good alternative.

These new shoes are so tight that it makes my feet sore. /that it causes sores on my feet