Answer
Wa `alaykum as-Salamu wa Rahmatullahi wa Barakatuh.
In the Name of Allah, Most Gracious, Most Merciful.
All praise and thanks are due to Allah, and peace and blessings be upon His Messenger.
In this fatwa:
As for your query, it seems that this is istihadah not menses. So, you can observe your period during which you should stop praying and sexual intercourse. After that,,you can do all this.
In his response to your question, Sheikh Ahmad Kutty, a senior lecturer and an Islamic scholar at the Islamic Institute of Toronto, Ontario, Canada, states:
Your persistent bleeding has nothing to do with menstruation; it is the case of what is known as istihadah or chronic bleeding.
You only need to stay away from prayers and conjugal relations (i.e. intercourse) during your monthly period or menses. To determine this, you should go by your habit prior to this chronic bleeding started.
In other words, if you had the habit of menstruating for six or seven days every month, that would be deemed as your period; you ought to perform ritual bathing (ghusl) and start praying afterwards; you are allowed to have intercourse, afterward.
If, however, the above was not the case with you, and you always had this persistent bleeding from early on then, you need to go by the maximum period of menses, which is fifteen days. Menses cannot exceed more than fifteen days, as ruled by eminent scholars.
Therefore, you ought to perform ghusl on the sixteenth day and resume prayers, etc., afterward.
Allah Almighty knows best.