Does ovarian cyst making stop my period for two months?

Possibly: The presence of hormonally active ovarian cysts can definitely have an effect on your cycle. If you period is absent, then you must check a pregnancy test. The workup would also include tests of thyroid function and measures of other hormones.

No: It is rare for an ovarian cyst to cause missed periods. Most ovarian cysts don't put out hormones so no effect on cycles.

Possible: "cyst" is a very general term, especially when talking about ovaries. It refers (correctly) to about 50 different possibilities. What doctors call "functional cysts" often produce hormones that can affect your cycle: a general rule of thumb is the bigger they are, the more likely to be active.