Does doxycycline monohydrate interfere with my implant nexplanon? if so, how long until my nexplanon is fully effective again? i only took the doxycycline for a week?

The idea that antibiotics interfere with hormonal birth control is overstated. It's not quite in the class of an urban myth, but it's close; actual interference is extremely rare. But of course you are free to use condoms for the next few days to provide an extra measure of protection. At your age condoms usually are a good idea for STD protection as well.