What is the ruling on my fasting for six months after I said, "I will not do a certain thing, otherwise I will fast for six months, or a curse from Allah"? And what should I do, as I am afraid and uneasy, and I have exams?

Your supplication of a curse upon yourself is forbidden and requires repentance. As for your statement, "If I do it, I will fast for six months," this is an oath of obstinacy and anger. Its ruling is that you have the choice between fulfilling it or performing an expiation for breaking an oath (kaffarat yamin), which is feeding ten poor persons or clothing them. If you are unable to do so, then fast for three days. The mentioned charity is not sufficient as expiation.