Hi Tanit,
The shall/will thing is rarely used in the US. The weird thing about it is that for first person, they reverse.
I shall is simply future. I will expresses determination.
He shall expresses obligation. He will is simply future.
There's a famous couplet to show the difference: I shall drown and no one will save me - a sad prediction. I will drown and no one shall save me - a delcaration of suicide with instructions to not stop it.
However, in the U.S., about the only time you'll hear "shall" is "Shall we [verb]?" Shall we go? Shall we dance?
Your teacher, if he was being very precise, was expressing future expectation, not determination.
I very much expect that if you surveyed 1000 Americans about the difference between "I shall" and "I will," well over 950 of them will say something like "Ummm.... is shall British, maybe?"