If so, then the general answer is that an IGH with more gears might help. But now, depending on how analytical you want to be, you can find out how to compute the gear inches on your existing bike, to make sure the new setup is actually an improvement at both ends of the range. I happen to be an extremely analytical person -- maybe pathologically so -- and wouldn't proceed without knowing the numbers.
On the other hand, I'm in exactly the same boat right now, and it has me shopping for a derailleur bike. I will continue to use the 3-speed IGH for easy riding around town, exactly what I built it up for.