Some babies do refuse the bottle because it hurts. If your doctor is not concerned, adding liquids to food sounds like a good idea. There is a lot of info out there -- just Google "teething baby won't drink" and you'll get lots of information.
I understand this is scary, but your medical professional can help. Please do not allow dehydration to be a problem -- go to the doctor if you suspect dehydration,
Livestrong
Dehydration and Teething in an Infant by ELIZABETH WOLFENDEN
Jul 26, 2011: Dehydration and Teething in an Infant The
teething process can cause infants a great deal of pain. Sometimes the
pain is so intense that infants refuse to feed, which puts them at a
greater risk of developing dehydration. Dehydration occurs when an
infant takes in less water than the amount leaving his body. Since
getting early treatment for infant dehydration is important, you
should take the time to learn how to spot the signs of dehydration so
you can seek treatment when necessary.
Signs of Teething
When your baby begins to feel a tooth coming in, he may be fussier
than usual. Some babies may simply whine a bit more than usual, while
others may be much more vocal. Babies who are teething often gnaw on
whatever they can get their hands on, which may include their own
fingers or toes, their toys or even you. You may notice that your
infant wakes more often during the night, has bulging gums or is
drooling more than usual. Infants may also develop a low-grade fever,
diarrhea or a cough when they are teething. Some babies refuse to
nurse or bottle-feed, since the sucking pressure may worsen their
teething pain. Refusing to nurse or bottle-feed may lead to
dehydration.