Praise be to Allah.
In the answer to question no. 50404 there is the ruling on the discharges that come from a woman’s uterus, in which we explained that the discharges that come from a woman’s uterus are taahir (pure), and what comes out from the urethra is najis (impure). In both cases the woman is required to do wudoo’.
Based on this, there is nothing wrong with you praying in this case, and you do not have to change or wash your clothes because this discharge is taahir.
The period during which your wudoo’ remains valid is the time of the prayer for which you did wudoo’. So you have to do wudoo’ for the prayer after the time for it begins, and your wudoo’ will remain valid even if this discharge comes out, until the time for that prayer ends, then you should do wudoo’ for the next prayer, and so on.
It is not permissible for you to pray two obligatory prayers with one wudoo’, unless you have joined them for one of the reasons for which prayers may be joined.
And Allaah knows best.