I'd say yes (although you may find you need some pretty extensive changes to get into a more upright riding position) - numbness is NOT good. But first try to get as much of the weight as you can off your back.

Try a messenger bag carried on your hip rather than a high-sitting backpack. A handlebar bag could carry some of your load. A seatpost-mounted rack could carry some, as well. (Provided your handlebars, stem and seatpost are alloy - if they're carbon you probably don't want to hang anything off them, but if you're thinking about replacing them for fit reasons anyway, there you are.)