Next time you finish or refill a prescription, keep the bottle and make your own travel sewing kit. The lid will stay secure and the bottle is big enough to hold all you will need.
Cut a small square of cloth and weave a couple of needles into it. Fold it over with the needle points inside and fasten with a couple of safety pins.
White and black thread will handle just about any emergency repair, but finding spools small enough to fit into a prescription bottle is quite a feat. Instead, wind them on straws. Just cut a couple of one inch pieces from a plastic straw, then cut a small slit on both ends of each one. Start winding thread on each one by pulling the beginning end through one slit. When you have enough, pull the end of the thread through the other slit to keep it secure.
If you don't have tiny scissors, a pair of nail clippers will snip thread or clean up a frayed area.
Slip it into your purse or pocket and don't worry!