On of the big advantages to drop bars is that you can change hand positions often. I can do much longer (time-wise) rides on my road bike than on my hybrid because my hands and arms don't fatigue being in one place the whole time.
Make sure you didn't pick up any bad habits from riding a bike with suspension: like locking your elbows or holding your shoulders tightly or holding your wrists bent rather than neutral. Those habits will be pretty uncomfortable on a standard fork bike, but you might be able to get away with them on a suspended fork bike.
Your upper body should float over the bike and your arms should feel springy. This will feel tiring in and of itself, because it uses your muscles and core control in new ways!
Also check your bar height relative to saddle height. Lots of women are much more comfortable with the bars at just about the same height as the saddle. (I like my bars to be about an inch higher than the saddle) The rule of thumb is that you should be able to pedal and "play piano" on the tops of your bars at the same time. If you are holding so much of your body weight on the bars/arms that you can't do this, there is a good chance your bars are too low, either for your body proportions or for your current core strength.
Putting too much of your body weight through the bars is also a disadvantage for bike control. If you hit a bump (for example) with too much on the bars that bump is going to really throw you off, much more than it would someone who can unweight their bars instantly and take the bump in stride.
Bars too low can also get you locking your elbows and craning your neck as your brain tries to bring your eyes up.
It's not too big a deal to raise your bars now and then lower them again as your muscles get used to the new position. Lots of women do that, too. So if you do get a taller stem, be sure to keep the shorter one, too. You might want it later!
Check out the book by Andy Pruitt, Complete Medical Guide for Cyclists. Lots of fit help there.
"If Americans want to live the American Dream, they should go to Denmark." - Richard Wilkinson