Have the doctors ever consider the headaches to be migraines. Migraine headaches are very debilitating and effect activities of daily living. I've had them so bad that my speech was slurred and required visit to ER for higher meds. Since then got a referal to neurologist and placed on a preventative med plus a rescue med.
It could be one of many possibilities.
Hope your daughter feels better
Welcome to the MedHelp forum!
Sinusitis involving the frontal and maxillary sinus can cause facial swelling that goes down with antibiotics. If the sinuses are really filled with a lot of fluid, it would need to be drained.
The swelling could also be due to water retention as in low protein in blood, kidney problems, severe anemia etc.
It could be due to hypothyroidism too (however your daughter may have had several tests). An autoimmune thyroid disease can be detected by doing a microsomal antibody tests. Diabetes Mellitus too can cause similar symptoms.
TMJ, dental infection, lymphedema (due to faulty lymph channel) are the other possibilities.
Since I cannot examine your daughter and know other related conditions you may be having, nor is a detailed history possible on net, I have listed the various possibilities that should be looked into. Please consult your PCP for primary examination followed by proper referral. Take care!