Is it permissible to expel phlegm and saliva with water while fasting, out of necessity, and does that invalidate the fast?

If introducing water to expel phlegm causes the water to reach the stomach, then this invalidates the fast and necessitates making up the days. However, if the phlegm causes shortness of breath and inability to speak, then the one who breaks their fast is excused and must make up the day. So, whoever vomits due to an excuse is permitted to eat and drink for the rest of their day. As for whoever vomits without an excuse, it is forbidden for them to do so in an obligatory fast, because it spoils their fast.