I am 19 years old and I am in love with my stepfather. He is not family to me but he is married to my mother. Are we allowed to be together in Islam? Can I get married to him or not?

Praise be to Allah, the Lord of the World; and may His blessings and peace be upon our Prophet Muhammad and upon all his Family and Companions.

For sure, it gives a feeling of pain both to soul and heart when an honest person becomes a mischief-maker a reliable caretaker becomes a sinful traitor. One, without a doubt, becomes amazed when he/she thinks about such a situation mentioned in the question. Then, how does it become agreeable to think of such a sinful relation and major evil!! Marrying a woman, being alone with her, looking with lust and then having sex with her prohibits marrying and having sex with her daughter. Such a prohibition is everlasting and the latter (daughter) becomes like his mother and sister. Allah Says (interpretation of meaning): {…your step daughters under your guardianship, born of your wives to whom you have gone in - …}[4:23].
As for Allah's statement: "Your step-daughters under your guardianship.", no one can deduce from such a verse that if some daughter is brought up in another family, she can marry her mother's husband. If you say: Why can we not understand the verse in its opposite conception, i.e. being raised in another house legalizes marriage? We answer you: in most cases, step-daughters are raised in their mothers' husbands house, and the verse comes in accordance with what is in daily life.
So, being raised under another's guardianship does not legalize the marriage of a step-daughter to her mother's husband. There is a consensus of opinion among Muslim scholars concerning this issue. Incest is one of the worst forbidden actions and hideous crimes for which a doer must be killed.
al-Baraa Ibn Aazib said: 'I met my uncle carrying a banner and I asked him about his destination'. He answered: "Allah's Messenger (Sallallahu Alaihi wa Sallam) sent me to a man who married his father's wife after the latter's death to cut off his head and to take his property". [al-Tirmizi, Abu Dawood, Ibn Majah, al-Nasa'i and Ahmad].
Thus, your love relation and your desire for marriage are strictly prohibited in Islam and the opposite of normal and sound human disposition and contrary to upright nature.
So, you have to repent and seek Allah's forgiveness for such an abominable deed. Also, you have to part from each other and each has to live alone and avoid meeting in any way. Because such a meeting constitutes suspicion and preventing it is an implementation of the Islamic principle than whatever is conducive to the Haram is itself Haram.
You have to remember Allah's Punishment and Resentment.
In addition, this girl has to seek a husband in accordance with the Sharia teachings, abandoning any form of doubtful relations and prohibited ties.
Allah knows best.