I wanted to marry this character, already did the quest she gave me,
though there is no such option in dialogue, my character has already equipped amulet of mara and other NPCs seem to be responsive to me.

What I want to know is, is this an actual bug or do some choices from past affect her decision of marrying me?

I googled her and found this . . .

http://elderscrolls.wikia.com/wiki/Carlotta_Valentia

"However, if the player sides with the Imperials, marriage is impossible."

EDIT: After reading further it appears as though you're in luck . . .

"A bug affecting all platforms causes the dialogue option involving marriage to not show up; even after completion of her quest. On PC, it is possible to fix this by opening the console, clicking her and typing "addfac 19809 1" (without the quotation marks(""))."

I am sided with Stormcloaks, also I read that on wikia too but was not sure whether the info was trustworthy or not, thanks.