Praise be to Allah.
We ask Allaah to heal you and make you well.
If your lips are harmed by using water when doing wudoo’, then you have to wash whatever you can of your face, and the other parts of the body that are to be washed in wudoo’, and then do tayammum instead of rinsing the mouth and washing the lips and surrounding area, because Allaah says (interpretation of the meaning):
“So keep your duty to Allaah and fear Him as much as you can”
You can do tayammum before or after doing wudoo’.
With regard to not doing wudoo’ at all, and doing tayammum only, that is not permissible, rather in this case you have to combine washing the healthy parts of the body with doing tayammum.
What we have said about wudoo’ applies also to ghusl. You have to wash your body and whatever you can of your face, as well as doing tayammum.
It says in Zaad al-Mustaqni’: Whoever has been wounded may do tayammum for that part, and wash the rest. End quote.
i.e., if a person has been wounded and cannot wash the site of the wound, then he should do tayammum for that, and wash the rest of his body that is healthy.
The basic principle concerning that is that if a person is wounded or burned in a part of the body that is washed in wudoo’, or has some sickness there, such cases fall into four categories:
1 – When it is uncovered and washing it will not harm it. In that case it is obligatory to wash it.
2 – When it is uncovered and washing it will harm it but wiping it will not. In that case he must wipe over it.
3 – When it is uncovered and both washing and wiping will harm it. In that case he should do tayammum for that part, and wash the other parts.
4 – When it is covered with a dressing etc that is essential. In that case he should wipe over the covering, and do the rest of his wudoo’, and not do tayammum.
Fataawa Arkaan al-Islam by Shaykh Ibn ‘Uthaymeen, p. 234.
Shaykh Ibn Baaz (may Allaah have mercy on him) was asked about a person who did wudoo’ but his hand was injured and could not be washed with water, and he forgot to do tayammum for it and prayed. He said: If there is a wound in one of the places that must be washed in wudoo’, that cannot be washed or wiped because that will lead to the injury being made worse or a delay in recovery, then this person must do tayammum. If a person does wudoo’ and misses a spot because of a wound, and starts to pray, then during the prayer he remembers that he did not do tayammum, then he should do tayammum and repeat his prayer, because what he did of prayer before doing tayammum is not valid… End quote from Majmoo’ Fataawa al-Shaykh Ibn Baaz, 10/197.