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 is His slave and Messenger.
If the imperfection related to your Tawaaf is only what you mentioned that you walked very fast, then your Tawaaf is valid as it is not a condition for the validity of Tawaaf that a person performs it while walking normally or with quick steps. What is important is that he performs Tawaaf 7 times with the intention of doing so, while being in a state of ritual purity and while covering his ‘Awrah.
However, it is desirable in Tawaaf Al-Qudoom (Tawaaf of arrival, i.e. the Tawaaf which the pilgrim performs for his Hajj when he reaches Makkah) that a person performing Tawaaf walks quickly with short steps during the first three rounds and normally during the remaining rounds. For more benefit, please refer to Fatwa 113111.
Allaah Knows best.