All perfect praise be to Allaah, The Lord of the worlds. I testify that there is none worthy of worship except Allaah and that Muhammad, sallallaahu ʻalayhi wa sallam, is His slave and Messenger.
The way in which you recite the Tahiyyaat and Tashahhud is fine and sufficient, by the will of Allaah, according to the opinion of many scholars.
An-Nawawi wrote:
“The shortest acceptable version of the Tahiyyaat is that which was cited by (Imaam) Ash-Shaafiʻi and most of the Shaafiʻi scholars. It is to say: 'At-Tahiyyaatu lillaah; salaamun ʻalayka ayyuha an-nabiyy wa rahmatullaahi wa barakaatuh; salaamun ʻalayna wa ʻala ibaadillaah as-saaliheen, ashhadu alla ilaaha illa Allaah, wa anna Muhammadan rasooluh.' ... Ibn Surayj said that the shortest acceptable version is: 'At-Tahiyyaatu lillaah; salaamun ʻalayka ayyuha an-nabiyy; salaamun ʻala ibaadillaah as-saaliheen; ashhadu alla ilaaha illa Allaah, wa anna Muhammadan rasooluh.'” [Ar-Rawdhah]
In the future, try to add the word ʻabdoohu (His slave) and say: ‘...wa ashhadu anna Muhammadan ʻabdoohu wa rasooluh.’ (...and I bear witness that Muhammad is His slave and messenger.) This addition is authentically reported in the hadeeth that was narrated by ʻAbdullaah ibn Masʻood which is the most authentic hadeeth reported about the Tashahhud. It should be noted though that the Tashahhud without the word ʻabdoohu is sufficient, as has been stated by the Shaafiʻi scholar Ar-Ramli . He wrote, “In fact, saying: 'wa anna Muhammadan rasooluhu' is sufficient; as I do not know of anyone who stated that the word ʻabdoohu is an essential part of the Tashahhud...” [Haashiyat Ar-Ramli ʻala Asna Al-Mataalib]
Allaah knows best.