My son just started working a 12 hour shift. He will work a total of 144 hours in this period of 15th to the 1st of August. It will be over a 3 week period of time and was told he would get 28 hours of OT and the rest is straight time.In this period of time he is also covering 24 hours for someone else on his time off.The 24 hours for someone else is included in the 144.Should he get more overtime for this or is it a week to week situation.

Overtime is a function of federal law (FLSA). It is based on hours actually worked during the workweek. All hours actually worked past 40 in the workweek generally have to be paid (at least) a 50% premium against regular rate of pay.

Your question as asked does not have an answer. You are talking about things like 12 hour shifts and 144 hours worked over what looks like a semi-monthly pay period. Overtime is not based on these things. It is based on the workweek. I am including a pointer to the federal DOL rules on the subject. I am not saying that maybe more overtime might be due. I am saying that you have not included the correct information to answer your question.

http://www.dol.gov/esa/whd/regs/compliance/whdfs23.pdf