We have already explained in the answers to more than one question that it is haraam for a man to have a relationship with a non-mahram woman outside the framework of marriage. See the answer to question no. 23349 and 9465.
The haraam things that the people who have these relationships fall into include: betrayal, being alone with a non-mahram member of the opposite sex, touching and looking; these are the ways that lead to falling into the sin of zina (fornication, adultery). This is in addition to the harmful effects it has on the heart, causing confusion and distracting it from the purpose for which it was created.
You say that you still meet this girl, and the results of these meetings are obvious to anyone with common sense. You have to persist in your repentance from your former relationship with her, and cut off all ties with this girl.
The solution to such a problem is to marry this girl, thus foiling the Shaytaan and protecting yourself from falling into sin. The Prophet (peace and blessings of Allaah be upon him) said: “We do not think there is anything better for two who love one another than marriage.” Narrated by Ibn Maajah, classed as saheeh by al-Albaani in Saheeh Ibn Maajah, 1847.
What this hadeeth means is that the greatest remedy for treating love is marriage, because this is the only cure for it. See Fayd al-Qadeer by al-Mannaawi, 295.
But you say that you cannot marry her, so you have no choice other than to be patient, strive to control your nafs (self), and keep yourself busy so that you will not think of her. Your marriage to someone else may be the means of your forgetting her, and you should avoid meeting her as much as you can.
You should know that the life of this world is very short, and the shortest thing in this life is haraam pleasure and the moments in which a person disobeys his Lord. But the joy of the Hereafter will last forever, so how can a smart person like you sacrifice that eternal joy for a moment of brief pleasure that will blacken the record of his deeds?
You should know that Allaah may decree death for you when you are alone with her, so how will you meet your Lord in such a state? What will you leave behind of shame and scandal for your family and for hers?
You should know that Allaah may punish you through your daughter or sister, because you were content to besmirch the honour of another, so you may expect the punishment of Allaah in this world rather than the Hereafter. Allaah protects the family and children of the righteous Muslim by means of his righteousness, but if a man is corrupt the only result can be is that his family and sons and daughters will be corrupt too. How can it be otherwise when he has set them the example by his own actions?
There is no way to forget about this girl except by filling your heart with the love of Allaah and fear of His punishment, and trying to keep the blessing of Allaah from being diminished because of this sin. Think about the consequences of this action whether in this world or in the Hereafter. Hasten to give up this sin and seek the reward for that with Allaah, so that you will then see – in sha Allaah – the blessings of faith, piety and delight in worship that your Lord will bestow upon you.
And Allaah is the Guide to the Straight Path.