Is what the questioner did correct by performing ghusl after seeing the white thread and considering what followed as istihada, given that her period is irregular and she takes medication to regulate it, and she does not recall the details of when the brownish discharge and later the pink thread appeared?

One of the two signs of purity (the white discharge/the white thread) has appeared. Therefore, any yellowish or brownish discharge that appears afterward is not considered menstruation unless it occurs within the customary period.

As for the blood mentioned, it is not considered part of the previous menstruation due to exceeding fifteen days (the maximum duration of menstruation), nor is it a new menstruation due to the absence of a complete period of purity between it and the previous menstruation.

Accordingly, she is considered to be experiencing irregular bleeding (istihada), and she must revert to her previous customary period if she has one. If she does not have a customary period, she should distinguish menstrual blood by its characteristics (its color, smell, and consistency). If she has neither a customary period nor the ability to distinguish, then she should estimate six or seven days of each month (the predominant custom of women), then perform ghusl, and she will be considered to be experiencing irregular bleeding for the remainder of the month.