Praise be to Allah.
We have previously explained that it is haraam to form relationships between men and women and for them to correspond for the purpose of getting to know one another, in the answers to questions no. 34841 and 82196. That is because of the fitnah (temptation) and infatuation that result from that, and because it may lead to direct contact and the haraam words and actions that may result from that.
In Fataawa al-Lajnah al-Daa’imah (17/67) it says: It is not permissible for you to correspond with a young man who is not your mahram to get to know him, because that is something that leads to fitnah (temptation) and to evil and corruption. End quote.
The peace of mind or feeling comfortable that you mention is something that is to be expected, because humans are created to be inclined towards the opposite sex, so you want that and like it and feel comfortable with it. Then comes the fitnah that we have warned about. The Prophet (peace and blessings of Allaah be upon him) said: “This world is sweet and green, and Allaah will make you successive generations therein, so look at what you do. Beware of this world and beware of women, for the first fitnah (trial) among the Children of Israel had to do with women.” Narrated by Muslim (2742).
Hence you have to repent to Allaah and stop this correspondence and contact, because this girl is a non-mahram who is not permissible for you. She should also understand this fact. A happy marriage cannot be based on sin and transgression of the sacred limits.
There is nothing wrong with marrying this girl after asking about her religious commitment and character and her family’s circumstances. If she is religiously committed and of good character, and her corresponding with you was a slip, then pray istikhaarah, asking Allaah for guidance, and go to her wali (guardian) and propose marriage to her.
After you have asked about her, you may find a suitable way to tell your mother about her, such as finding a girl who is known to some of your relatives and friends and so on, because telling her that you got to know her via the internet may be a reason for rejecting her.
We ask Allaah to help you to choose a righteous wife who will make you happy and help you to obey Allaah.
And Allaah knows best.