What you've been reciting after Durood-E-Ibrahim is called "Dua-E-Koonoot" (Allahumma inna nastainuka, wanastagfirukka....). We recite that in "Salaat ul Beet'ir" on third rak'at after an extra takbir.
And the Du'a you are looking for to recite after Durood-E-Ibrahim, is called
اللَّهُمَّ إِنِّي ظَلَمْتُ نَفْسِي ظُلْماً كَثِيراً، وَلَا يَغْفِرُ الذُّنُوبَ إِلَّا أَنْتَ، فَاغْفِرْ لِي مَغْفِرَةً مِنْ عِنْدِكَ وَارْحَمْنِي إِنَّكَ أَنْتَ الْغَفُورُ الرَّحِيمُ
Allahumma inni zalamtu nafsi zulman kathiran wala yaghfirudh-dhunuba illa anta, Faghfirli maghfiratan min indika war-hamni, innaka antalGhafur-Rahim
O Allah, I have greatly wronged myself and
no one forgives sins but You.
So, grant me forgiveness and have mercy on me.
Surely, you are Forgiving, Merciful
This Du'a was taught by our Prophet(PBUH) Bukhari :: Book 8 :: Volume 75 :: Hadith 338
Narrated 'Abdullah bin 'Amr:
Abu Bakr As-Siddiq said to the Prophet,
"Teach me an invocation with which I may invoke (Allah) in my prayer." The Prophet said, "Say: Allahumma inni zalamtu nafsi zulman kathiran wala yaghfirudh-dhunuba illa anta, Faghfirli maghfiratan min indika war-hamni, innaka antalGhafur-Rahim."
But there is no rule that this is the only Du'a that should be recited. You can recite any valid Du'a in Salah before Taslim. It is your preference.
P.S: In case you need the recitation of the the Du'a, here's the direct download link of an mp3 file. It contains recitations of all the Du'a you'll need in Salaat along with the English translations