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.
Since you are certain that you did not have any discharges during Tawaaf (circumambulation around the Ka’bah), then your ‘Umrah is valid, Allaah willing; we ask Allaah to accept our good deeds and yours.
As regards Sa’y (walking between mounts As-Safa and Al-Marwah), it is not a condition for its validity to be in a state of purity, i.e. in a state of ablution or performing Ghusl (a ritual bath) if one is in a state of sexual defilement, but this is a condition for the validity of Tawaaf.
Furthermore, the discharge which you mentioned in the question does not seem to be menses. Discharge is considered as menses if there is blood and it lasts for one day and night, in a way that if you insert a piece of cotton or the like, it comes out dirty [with blood] and on the condition that there is between it and the last menses (at least) fifteen days.
For more benefit, please refer to Fataawa 91444, 98693 and 129266.
Allaah Knows best.