Should I worry if Braxton Hicks contractions become more painful? What should I do? When should I call emergency?

As long as it's not early labour and the contractions doesn't increase in intensity and frequency (just dull ache), strictly speaking there's no need to worry because it's common. If you're worried or unsure, please see your gynae. One of the things the doctor may eventually even do is to assess that your cervix is not opening up by internal examination. If your cervix is opening up with mild contractions, this predicts that you may be going into labour soon. If you're not due yet (e.g 32 weeks), this could mean premature labour and early action can stop labour from progressing.