In "Two Swords" (Game of Thrones, S04E01), Qyburn asks Cersei whether her "symptoms" had gotten better. When Jaime asks her about this, she refuses to tell him. They then engage in an argument in which Cersei tells him that he has arrived "too late". At the time, I assumed it was because she is engaged to Loras Tyrell but I wonder if that's not the only reason.
I could be wrong, but I don't think this is ever made explicit. I can think of several possible explanations:
- Cersei is pregnant and experiencing something akin to morning sickness. Jaime is too late in the sense that Cersei has found other lovers. I think this is the most likely scenario. That the symptoms go away indicates either she wasn't really pregnant or Kyburn helped effect an abortion.
- Cersei became infected with a sexually transmitted disease for the same reasons mentioned above.
- Cersei is going through menopause as you mentioned, or is perhaps faking menopause to get out of her engagement with Ser Loras (this wouldn't make as much sense since the symptoms seem to abate).
- Some other illness, and it was only mentioned because Jaime would be jealous that a non-maester touched her.
In the episode Eastwatch, she reveals to Jamie that she's pregnant.