Salam aleykum all4islam.First of all welcome to Islam..I think if you find a scholar imam to ask the question is the best way or search through the internet since you'll find some different answers from different people here , you are alread given two different opinions.Mine is different too.In Islam your past sins are forgiven when you enter the religion.And acording to opinion of the majority no matter wether trinitarian or not the christians are considered the people of Book.Therefor 'I think' you can marry to her.But as caryon stressed, flirting is not helal in Islam.If you want to marry, go and tell her directly that you want to marry and wait for the answer.