"God" is general term it can refer to any god. and "oh, my god" has become a normal words people use in their daily lifes. But how often did you heard people call their God as "Allah" expect from people who follow samawi religion?
I hope you can change them somehow {but I think that's too late) or not doing the same mistake in the future.
"Allah" is not exclusive to Islam whatsoever. "Allah" literally means "God" and has literally the exact same function as "god" has in English. Arabic-speaking Christians and Jews use the word "Allah" to refer to the Judeo-Christian god of the Torah and Bible, and Arabic translations of the Bible use the word "Allah." Arabic-speaking Sikhs and polytheists use "allah" to refer to their gods as well. It also predates the Muslim religion by hundreds if not thousands of years. Muhammad's own father's name was Abdullah, or Abd-Allah, meaning "servant of god," and obviously he was named before his son was born.
I'm not trying to be mean or anything, but "allah" is not a word that belongs to Islam any more than "god" belongs to Christianity. Being offended by the use of the word "allah" in this case is the same as when Christians get offended by someone saying "Oh my god."