YOU SAID:
I forgot my Birthday was today...
INTO JAPANESE
私の誕生日が今日だったのを忘れていました...
BACK INTO ENGLISH
I forgot my birthday was today ...
INTO JAPANESE
私の誕生日が今日だったことを忘れていました...
BACK INTO ENGLISH
I forgot that my birthday was today ...
INTO JAPANESE
私の誕生日が今日だったことを忘れていました...
BACK INTO ENGLISH
I forgot that my birthday was today ...
That didn't even make that much sense in English.