תרגום - טורקית-אנגלית - askım ya kocayi buldun beni unutun seni çok...

I think; "ya" here is not the word for "whether.. or.." Instead, it is a word used in colloquial language and doesn't have an meaning in itself.
So "or" should be removed because the meaning changes. It should only be "My love, you found a husband (and) you forgot me"

must be 'you found a husband then you forgot me'

Dear cheesecake,
How can we forget to use the word "ya=or" ? Does to find a husband mean to forget somebody ?

No of course, I try to mean, if the sentence "ya koca buldun ya da beni unuttun" then your version would be right, but the original text doesn't include "ya da". You know that in Turkish we cannot use "ya" (meaning that weather/or) on its own; it should be accompained by "ya da" as well.
So, this "ya" is a vulgar word (like we use in "hadi yaa" )