What size tires are you currently running on the FX and what's their maximum tire pressure? Lowering tire pressure is the cheapest and easiest solution to making your bike a little more comfortable. So long as you don't lower them too much, that's where I'd start. What gloves are you using at the moment? If you aren't already using a padded glove, you might try them. Better grips might also help. I'm not expert on flat bar handlebars, but there are other ladies on TE that might have some suggestions in that department.
I'm hestitant to encourage you to spend any money on the FX to upgrade it, at least not until you've got more miles under you. After-market carbon forks aren't cheap, and the choices on the market are also not endless unfortunately. And in the end, you may not see the improvement you're hoping for. Carbon forks help, but there's only so much you can do with some aluminum bikes. There are also differences among carbon forks. I've used some that ride very nicely, while others have been very stiff and unforgiving.
I went very quicky from an FX to a road bike, so like Hebe, I wouldn't be surprised to see you end up on one yourself in fairly short order, but getting the right fit on a road bike is generally more complicated than it is on a hybrid, so I'd be careful in looking at used bikes at this point. You might be better off working with a good LBS in your area.
I think the general perspection is that road bikes are far more aggressive than hybrids. I don't actually find that to be all that true. It all depends on the road bike. Mine are set up to be fairly relaxed. I much prefer drop bars for the variety of hand positions they afford. That said, get some miles on your FX before you do anything radical or costly.
Live with intention. Walk to the edge. Listen hard. Practice wellness. Play with abandon. Laugh. Choose with no regret. Continue to learn. Appreciate your friends. Do what you love. Live as if this is all there is.
--Mary Anne Radmacher