But, if it's an illness, what is the fiqh law about this kind of situation? I heard that I have to keep a bottle of water near me during my salat, and when I pass gas, I just have to do wouzou and continue my namaz. Is it true please?

If there was an illness of continuous passing gas without an intermission of pause that allows a person to do wodhu and pray, then one can do the wodhu and pray and ignore any gases passed during the Salaat.

However, if a person have some intermittent time or a pause in which the gases stop and that pause was enough to do wodhu and pray limiting on the wajibaat then one must choose that time to pray as long as that pause is not out of the time range of the Salaat.