Since your daughter is 14, her body is going through a lot of hormonal changes and that can lead to changes in allergies. Seasonally, she can be more affected by them. Since we have had sooo much rain, mold could be a culprit. However, diet can greatly affect a person. Even if you don't detect a food allergy, I would consider it and an easy way to determine if she has a food allergy is to remove that food from her diet. I witnessed this with two people who are very close to me.
My sister for years suffered with major sinus problems, terrible headaches/migraines, severe fatigue,etc... which began in her teens. Every few months lead her to another round of antibiotics. She is also a cheese-a-holic. Two years ago, her doctor suggested that she remove dairy from her diet for 2 - 3 weeks. What you crave can actually be your culprit. Amazingly, she felt so much better after 2 weeks and, now, two years later, it has had a dramatic improvement on her life.
Secondly, gluten allergies are becoming more prevalent. Someone I know had a young, teen-age daughter who was debilitated with severe migraines and sinus concerns for 5 months. She could barely lift her head off a pillow when they hit. She has dealt with headaches, on and off, for years but nothing like this. She received chiropractic care, had CAT scans, MRI's, medicines, vitamins but nothing worked. An amazing number doctors later, she saw a nutritionist/allergist who diagnosed her with a potential gluten allergy. That was 5 months ago. She is totally off gluten. She "cheated" after her diagnosis, as teens would, then realized that her headaches would return. It's great to see her healthy again.
Medication does help but to determine the underlying cause of her concerns would really help your child. Even seeing if there are any changes that you can make to your home (i.e. having a home hepa filtering system attached to your furnace or buying a better furnace filter, having hardwood/tile floors, keeping all pets out of her bedroom-if you have any). I have bad allergies and there is nothing like it when they are under control. I have to work hard to keep it that way! Neti-pots are great but I know I have a teen and she is challenged in doing the technique. However, at the very least, if her allergies hit, have her gargle with warm/hot water, with Kosher salt (it has to be Kosher or Sea salt because table salt has too many chemicals) and a tiny pinch of baking soda. Make the water as hot as she can tolerate and gargle for 30 seconds. I just pop a little dish in the microwave. You can even buy one of those bulb syringes and this will create your own neti-pot. Do the nose part, first, then gargle second - encourage her to do it 3 - 4 times a day if she is symptomatic.
Good luck.