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

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 after doing 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 tayammum without suppressing the need to relieve
oneself is better than praying with wudoo’ 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, according to scholarly consensus.

End quote from Majmoo‘ al-Fataawa, 21/473 

Shaykh Ibn ‘Uthaymeen (may Allah have mercy on him) said: If
someone were to ask: A man has wudoo’ but is suppressing the need to urinate
or pass wind, but if he does so he does not have any water with which 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 is no 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.