Must I continue fasting, knowing that fasting may lead to prolonged and irregular bleeding, which causes a deterioration in health such as anemia and lethargy, especially since the bleeding started before the usual time of my period?

If fasting causes you bleeding and apparent harm, such as anemia, strive to treat it. If your condition does not improve with treatment, then it is permissible for you to break your fast.

If there is hope for your recovery, you must make up the days you missed later, as Allah says: ﴿So whoever among you is ill or on a journey [during them] - then [he must make up] an equal number of other days.﴾ [Al-Baqarah: 184].

However, if there is no hope for your recovery, then you are not required to make up the fasts. Instead, you should feed a poor person for each day, as Allah says: ﴿And upon those who are able to fast [but with difficulty] - a ransom [as substitute] of feeding a poor person.﴾

As for slight lethargy and mild headaches, they do not permit breaking the fast, as this is a common occurrence. The illness that permits breaking the fast is severe, one that worsens with fasting or for which recovery is feared to be delayed.