Must I divide my first salary equally among my family—as I swore—if I am accepted into college, despite my need for it, and is it permissible to postpone the division until I am able?

If what you uttered was an oath conditional upon acceptance into the college, and you swore by one of the names of Allah the Almighty or one of His attributes, and you were accepted into the college, then one of two things is incumbent upon you: either you fulfill your oath and divide the first salary as you swore, or you expiate for your oath.

If you do not divide the first salary, then you have broken your oath, and you must offer an expiation for an oath (kaffarat yamin): feeding ten needy persons or clothing them, or emancipating a slave. If you cannot find these, then fasting for three days. This applies if you did not have a specific intention when you swore the oath. However, if you did have an intention, then the oath is restricted by it, and there is no breaking of the oath unless you violate what you intended.

The majority of scholars hold that it is not permissible to delay the expiation without an excuse, whereas the Shafi'is permit its delay.

If what you uttered was intended as a conditional vow of recompense upon acceptance, please clarify; because a vow requires a formulation that indicates commitment to an act of worship.