The other aspect is you may want to focus on your riding mechanics, that is how your body is moving and what is your body doing. Do this with a good trainer. You should not be holding the handle bar in death grip. this also maybe indicative of improper fit on your bike. Another thing, is you should also not be throwing your butt off the back off the seat. another indication of improper fit. I could see how this could cause you to skrunch your shoulder and neck and give you a horrible headache.

A good trainer or coach can see how you could improve your riding style especially going uphill. Most just don't ride uphill in an efficient manner. And some, would like you to grind away in big gears, others prefer that you go uphill by spinning. For us women, its better to spin up a hill. Our joints are too flexible to grind away in big/tall gears. We also don't have the brute strength like men to do so.

Riding uphill requires you to conserve your oxygen use by relaxing your shoulder, arms, wrist and hands except on really steep hill where you need to be pulling on the bars. And if you look at a good climber, you will see that their face goes blank from relaxing all the facial muscles. Also you need to breath deeply from the bottom of your lungs. Deep breathing. I was also told to breath in from the nose and exhale from the mouth. Exhale should be quick almost like a cough. Don't exhale by tightening your neck and throat. Breath in slower, longer and deeper. All of this comes from practice and training. Look at some videos of pro riders on mountain stages and see how they ride. Picture yourself making the same body movement when you go uphill then talk to find a right trainer/coach. Riding technique has much to do as strength when going uphill.

Another trick of riding long hill is to make short goals going up hills. To the next telephone pole. to the rock just up ahead, to the pot hole I see 20 yards away... Life goal isn't made in big giant step. It's lot of little steps. Riding uphill is the same thing.