What is the spindle length of the original BB (if you still have it)? The bike shop should have measured that length before selling you a 113mm one. I assume you are using a square taper BB, right? If so, then the only issue should be going back to the bike shop, tell them they sold you a BB that is not long enough, and that you want to exchange it for a longer one. The shell width should not be that big of an issue, so if the BB is a 68 or 70, you should be able to get that to work, but you might want to measure the bottom bracket part of the frame (not the actual bottom bracket component) in order to get the accurate shell dimension for when you go exchange it. But, as I said, the issue should be resolved by getting a longer spindle BB, assuming you are using the original crank arms. If you are using different crank arms, then those might be also causing a problem, but probably not, and I would have to actually inspect them to give direction.
Go back to the shop and tell them they screwed up, especially if they had your bike in the shop when they sold it to you.