It's not that wrong because "바람에" and "때문에" sound like "바라메" and "때무네" respectively.^^
As to both phrases, there is a pattern which you are worth memorizing which is...
1) A 하는 바람에 B 했다.
B = something bad happened because of A
This phrase is often used for nagative sentences or in written.
For example,
그는 자주 지각하는 바람에 해고당했다.
He was late often,so he got fired.
Something bad happened = 해고 당했다.
The reason = 자주 지각하는 바람에
2) A 하기 때문에 B 하다/한다/했다.
A is the main reason why you did/do B or why something should be B.
For example,
매일 운동하기 때문에 건강하다.
= Because of working out every day, I am very fit.
The main reason for "건강하다" is "매일 운동하기 때문에"
9시까지 출근해야 하기때문에 나는 아침밥을 먹지 않는다.
I miss breakfast because I have to be at the office by 9.
The main reason for "아침밥을 먹지 않는다" is "9시까지 출근해야 하기때문에"
^________^