If using water will make you sick, then it is permissible for you to do tayammum.
The Standing Committee for Research and Issuing Fatwas was asked:
What is the definition of sickness whereby it is permissible to do tayammum even though water is available?
The Committee replied:
It is sickness where there is the fear that using water may make the sickness worse or delay the healing of wounds.
Fataawa al-Lajnah al-Daa’imah, 5/345
The ruling on urinary incontinence and continual passing of wind is the same as the ruling on istihaadah (prolonged non-menstrual vaginal bleeding). Urine, wind and vaginal bleeding all invalidate wudoo’, and Allaah says (interpretation of the meaning):
“Allaah does not want to place you in difficulty, but He wants to purify you, and to complete His Favour to you that you may be thankful”
“Allaah intends for you ease, and He does not want to make things difficult for you”
So people suffering from these problems are allowed to do wudoo’ for each prayer when the time for that prayer has begun, then they should pray as they are, even if some wind, urine or blood comes out of them whilst they are praying.
This ruling is for one who passes wind continually. If that is intermittent, and he can do the prayer during the time when it stops, then he has to do wudoo’ and pray at the time when the wind has stopped.
Shaykh Ibn ‘Uthaymeen said: There are two scenarios with regard to one who suffers from urinary incontinence:
1 – If it is continual and does not stop, and every time something collects in the bladder it comes down, then he should do wudoo’ when the time for prayer has begun, then put something over his private part and pray, and it does not matter what comes out.
2 – If that happens after he urinates, or ten minutes or quarter of an hour after that, then he should wait until it stops, then do wudoo’ and pray, even if he misses the prayer in congregation.
The basic principle is that wudoo’ should be done after the time for the prayer has begun.
It was narrated that ‘Aa’ishah said: Faatimah bint Abi Hubaysh came to the Prophet (peace and blessings of Allaah be upon him) and said, “O Messenger of Allaah, I am a woman who suffers from istihaadah (prolonged non-menstrual vaginal bleeding) and I never become pure. Should I give up praying?” The Messenger of Allaah (peace and blessings of Allaah be upon him) said: “No, rather that is a vein and it is not hayd (menstruation). When your period comes, stop praying, and when it goes away, wash the blood from yourself and pray, then do wudoo’ for every prayer until that time [of menstruation] comes.”
Narrated by al-Bukhaari, 226; Muslim, 333
With regard to prayers where doing wudoo’ after the time for them begins is difficult, such as Jumu’ah and Eid, it is permissible to do wudoo’ shortly before the time begins.
The Standing Committee was asked about a man who passes wind continually – how should he do wudoo’ and pray?
The Committee replied:
If your situation is as you describe, and you suffer from continual wind, then you have to do wudoo’ for each prayer after the time for the prayer begins, then it does not matter what comes out of you after that. With regard to Jumu’ah, do wudoo’ for it before the khateeb comes in, which will enable you to listen to the khutbah and perform the prayer.
Fataawa al-Lajnah al-Daa’imah. 5/412
If it is difficult for you to do wudoo’ for every prayer and offer the prayer on time, then it is permissible for you to join Zuhr and ‘Asr and pray them at the time of either with one wudoo’, and to join Maghrib and ‘Isha’ similarly with one wudoo’
The Prophet (peace and blessings of Allaah be upon him) granted a concession to the women who suffered from istihaadah, allowing her to join her prayers. This was classed as saheeh by al-Albaani in Saheeh Abi Dawood, 284
You can pray qiyaam al-layl – Taraaweeh – with the wudoo’ you did for ‘Isha’.
Shaykh Ibn ‘Uthaymeen (may Allaah have mercy on him) was asked:
Is it permissible for a woman who is suffering istihaadah to pray qiyaam al-layl with the wudoo’ of ‘Isha’ if half the night has passed?
This issue is one concerning which there is a difference of opinion. Some scholars say that if half the night has passed, she must repeat her wudoo’. And it was said that she does not have to repeat her wudoo’, which is more correct.
Fataawa al-Mar’ah al-Muslimah, 1/292, 293
With regard to Duha prayer, the time for it is limited, so it is essential to do wudoo’ for it after the time has begun. It lasts from a quarter of an hour after the sun has risen until approximately quarter of an hour before Zuhr.
And Shaykh Ibn ‘Uthaymeen (may Allaah have mercy on him) was asked:
Is it permissible for that woman to pray Duha with the wudoo’ she did for Fajr?
That is not permissible, because there is a limited time for Duha prayer, so it is essential to do wudoo’ for it after its time has begun. This woman is like one who suffers from istihaadah, and the Prophet (peace and blessings of Allaah be upon him) commanded the woman who suffered from istihaadah to do wudoo’ for each prayer.
And Allaah knows best.