You can do water changes, but make sure you replace the medication that would have been removed with the water. If you remove 1 gallon of water, put in 1 gallons worth of medication after the change.
If your tank is filtered and you use activated carbon, make sure you remove that from the filter as it will filter out the medication.
As for the jumpiness, they can get high-strung if water conditions change (such as adding medication) or if they are sick. I wouldn't worry too much about that, some bettas are moody. Mine sometimes practically jump out of the tank when I walk by (they think i'm going to feed them), and sometimes are too busy to notice.