There are some things that are recommended to say after you finish your Tashahhud and Salawat to the Prophet. Some of the duas are:
اللَّهُمَّ إِنِّي أَعُوذُ بِكَ مِنْ عَذَابِ جَهَنَّمَ وَمِنْ عَذَابِ الْقَبْرِ وَمِنْ فِتْنَةِ الْمَحْيَا وَالْمَمَاتِ وَمِنْ شَرِّ فِتْنَةِ الْمَسِيحِ الدَّجَّالِ
Meaning: O Allaah, I seek refuge with You from the punishment of Hell and the punishment of the grave, and from the trials of life and death and from the worst of the turmoil of the Dajjaal.
اللَّهُمَّ إِنِّي أَعُوذُ بِكَ مِنْ عَذَابِ الْقَبْرِ وَأَعُوذُ بِكَ مِنْ فِتْنَةِ الْمَسِيحِ الدَّجَّالِ وَأَعُوذُ بِكَ مِنْ فِتْنَةِ الْمَحْيَا وَفِتْنَةِ الْمَمَاتِ اللَّهُمَّ إِنِّي أَعُوذُ بِكَ مِنَ الْمَأْثَمِ وَالْمَغْرَمِ
Meaning: O Allaah, I seek refuge with You from the punishment of the grave and I seek refuge with You from the turmoil of the Dajjaal and I seek refuge with You from the trials of life and the trials of death. O Allaah, I seek refuge with You from sin and heavy debt.
اللَّهُمَّ إِنِّي ظَلَمْتُ نَفْسِي ظُلْمًا كَثِيرًا وَلا يَغْفِرُ الذُّنُوبَ إِلا أَنْتَ فَاغْفِرْ لِي مَغْفِرَةً مِنْ عِنْدِكَ وَارْحَمْنِي إِنَّك أَنْتَ الْغَفُورُ الرَّحِيمُ
Meaning: O Allaah, indeed I have wronged myself greatly, and there is none who forgives sins besides You. So grant me forgiveness from You and have mercy on me, for You are the All-Forgiving, Most Merciful
The first two duas have overlap, so you can probably combine them. It is also allowed to pray for yourself anything you wish after the Tashahhud and Salawat. So, there is nothing wrong in you making the dua you mentioned after seeking refuge with the first two duas.
For more information you could read this by IslamQA.