Don't burp them, you'll lose all the CO2. Don't get in a fret. There was only a tiny amount of oxygen in that headspace, and maybe none if it was used by the yeast. Don't worry so much, all will be fine.
EDIT: Rock hard is good, that means yeast has produced carbon dioxide (and a little bit more alcohol) from sugar. Amber bottles help keep light from impacting the beer, but it's best to keep the bottles in the dark.