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.
Dear sister, the situation you described contains many serious matters and we will try to address each according to their importance. First, the person who claims to recite the Qur'an on a patient and makes false accusations about the source of the troubles is not acting in accordance with Sharia or al-Ruqya al-Sharia (recitation of the Qur'an for treatment). Second, to spoil relations between persons is a bad practice. It is practiced only by one of two persons: either by a liar and juggler or by a magician and cheater, both the lie and magic are among major sins that spoil good relations.
No doubt, this is a trial; you should be patient and continually try to convince your female friend that you are far from her blame.
Continue asking Allah to show your innocence and believe in Allah that one day He will surely reveal the reality.
Concerning having a boyfriend, know, dear sister, that Allah forbids all kinds of relations between a man and alien woman except within the boundaries of legal marriage. Also, it is forbidden to work in a place where sexes mix except if there is dire necessity, and then one should abide by all the rules and regulation set by Sharia. No doubt safety from the problems you mentioned is in abiding by the rulings of Sharia.
Allah knows best.