That's a good question for school storage. There's with cap or without cap, obviously you want with cap. In our family we need syringes by the case. If you only need a couple a local medical supply store would probably have individuals for sale. The pencil box sounds good to me since it's a hard case that you can label.
What we did was buy a bag recommended by some kind soul here, a waterproof bag from Magellan's travel supply. On the outside we put a pic of child on label with name, medicines inside with dosage amount, parent contact info and allergens. Taped it all over with tough clear tape to repel liquids. On the inside we have epis, bottle of antihistamine, syringes, insurance card, EAP. The bag has a waist strap so the teachers can carry it around easily. In our case one medicine bag stays in the classroom, the other a teacher wears when they go outside the classroom.
In any case I'd load the pencil box with about 3 pre-loads of Benadryl in luer lock w/cap, scotch tape the cap in place. I'd label each tube with name and dose and medication contained within stating in bold "ONE DOSE" or similar, expiration date might be good idea, too. Then I'd label the outside well with whatever info you deem necessary, adding to the box whatever else goes in for child (epis, action plan, etc.).
Periodically I go in to the medicine bags at school to check on them, make sure everything looks good, fully stocked, expirations are still good. Our teachers are terrific on always carrying the bag but not the best at temp control.