I believe that the timing of the doses is about "leveling out" the effective background basal your body experiences.
Here is what I got when I did a quick google of the duration of activity for the current "big three" basal insulins.
Lantus: Glargine (Lantus): Onset, 1.1 hours. Peak, 5 hours. Duration, 24 hours.
Levemir: Insulin detemir: Mean duration of action of ranged from 5.7 hours at the lowest dose to 23.2 hours at the highest dose.
Tresiba: Insulin degludec: beyond 42 hours (??)
Lantus can actually start to "wear out" somewhere before 24 hours. That's why it is often split into two doses to provide a more constant & consistent background basal delivery of Lantus.
Levemir has a much shorter duration than Lantus. Usually it is around 12 hours and, thus, two doses per day. But some people split their Levemir into three doses. Unlike Lantus, for most people Levemir generally should be taken as at least two doses about 12 hours apart. Levemir just doesn't persist long enough to take it only once a day.
What makes Tresiba different from the other two is that its duration is apparently much longer than 24 hours. The claim Google stumbled upon was 42 hours.
Actually, I think Tresiba starts to fade and trail off much sooner than the claimed "42 hours". But since people structure their day around a 24 hour clock, Tresiba feels easier since it only has to be taken once a day to overlap its duration of activity and smooth out the effective basal.
Until you can accomplish the script wrangling needed to try Tresiba, can't you just take your morning Levemir shot earlier? Say, when you get up and then take the second Levemir dose sometime in the late afternoon/early evening after school?
This shtuff about having to go to the nurse's office is from my perspective a bunch of bureaucratic stupidity. You do it yourself the rest of the time, but suddenly while you are in school someone else needs to "help" you? Spare me. Puh-lease.
(Huh. It feels strange that you are now in the same time zone as I am. Oh, well. )