It is not a Q-factor issue but a gearing issue. The front derailer only has a limited range of swing and a limited reach. The range is the effective distance it can go between left and right and the reach how far it leans over to the right in order to work between it's two range limits. If your BB spindle is too long or too short, it could put the FD outside it's range or outside it's reach, meaning that you won't have great gear adjustment.
If you fit a 115 instead of a 113, you may not have a problem providing that the 113 was in the first place the correct one. Sometimes the bike's history is not known and you cannot rely on the previous BB in there to give you the correct length. The centre point of the FD's range within its correct reach is published as a number in mm called the chainline. This would be the line measured from the centre of the seat tube to the centre of the middle chainring on a triple or halfway spot between the two chainrings on a double.
Q-factor has an indirect bearing but one doesn't change a BB spindle length to fiddle with the Q-factor. The Q-factor is determined by tyre clearance at the chainstay and crank clearance at the outside of the chainstays and FD chainline then chosen according to that by the manufacturer.