Yes. In correct colloquial English that would be a better translation. But you probably know by now that the Vietnamese Duolingo module was not written/checked by native English speakers...
It would depend on how it is understood in Vietnamese.
"I am the first person to love her" = I loved her. She might or might not have loved me back. More context is needed. "I'm her first love" = She loved me and it's implied that I loved her back
What's the implication in Vietnamese?