Praying with tayammumis better than praying with a previous wudoo’ done using water when one is desperate to relieve oneself

I entered the mosque one day and there was water in my house to do
wudoo' for prayer, but I still had my wudoo'. However the need to
relieve myself was pressing and I could not find any water, and I was
afraid that I would miss the prayer in congregation, so I joined the
prayer.
Praise be to Allaah.
Firstly:
It is makrooh for the worshipper to start praying when he is
suppressing the need to defecate or urinate, because the Prophet
(blessings and peace of Allah be upon him) forbade doing that, because
of what it results in of failing to attain complete focus and
contemplation in prayer.
See the answer to question no. 8603
Secondly:
If the worshipper is suppressing the need to urinate or defecate and
he cannot find any water with which to do wudoo', it is better for him
to relieve himself then do tayammum and pray.
His praying with tayammum whilst having proper presence of mind and
focus is better than praying afterdoing wudoo' with water but without
proper focus, because the heart and essence of the prayer is proper
focus (khushoo'), so it is essential to maintain it.
Shaykh al-Islam Ibn Taymiyah (may Allah have mercy on him) was asked:
Which is better: praying with wudoo' whilst suppressing the need to
relieve oneself or to relieve oneself then do tayammum due to lack of
water?
He replied:
Praying with tayammumwithout suppressing the need to relieve oneself
isbetter than praying withwudoo' whilst suppressing the need to
relieve oneself, because praying when suppressing the need to relieve
oneself is makrooh and is not allowed, and there are two opinions
concerning its validity. But praying with tayammum is valid and there
is nothing makrooh in it, accordingto scholarly consensus.
End quote from Majmoo'al-Fataawa, 21/473
Shaykh Ibn 'Uthaymeen (may Allah have mercy on him) said: If
someonewere to ask: A man has wudoo' but is suppressing the need to
urinate or pass wind, but if he does so he doesnot have any water
withwhich to do wudoo'. Should we tell him to relieve himself and do
tayammum for prayer, or should we tell him to pray whilst suppressing
the need to urinate or pass wind?
The answer was:
You should tell him to relieve himself and do tayammum; he should not
pray whilst suppressing the need to urinate or pass wind. That is
because praying with tayammum is not makrooh, according to scholarly
consensus, but praying whilst suppressing the need to urinate or pass
wind is not allowed and is makrooh. And some of the scholars regarded
it as haraam and said: Prayer whilst suppressing the need to urinate
or pass wind is not valid, because the Messenger (blessings and peace
of Allah be upon him) said: "There isno prayer in the presence of food
or when suppressing the need to urinate or defecate." End quote from
ash-Sharh al-Mumti', 3/236
So the prayer that you offered is valid, in sha Allah, and you do not
have to repeat it.
And Allah knows best.