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.
First of all, you should know that the minimum period of menses is one day and one night [i.e. 24 hours], and the maximum period of menses is 15 days. Therefore, if the total period of these spots of blood which you saw lasted for one day and one night, then it is considered menses, and if it did not last for one day and one night, then it is not considered as menses in itself.
As regards the bleeding that you experienced after you came back from Hajj, then if by adding it to these (initial) spots (i.e. by adding all the sporadic durations of spotting together), it exceeds one day and one night and its totality along with the duration of cleanliness between them (i.e. between the initial spotting and the spotting which you experienced after Hajj) did not exceed fifteen days, then all this is menses.
But if the period between the two bleedings is 15 days or more, then the second (bleeding) is menses and the afore-mentioned details apply to these spots, so if they lasted for one day and one night, it is menses, and if its totality did not last for one day and one night, then it is not menses.
On the other hand, if the time period between the two bleedings is less than 15 days, and its totality along with the period of purity that you had between them, exceeded 15 days, then it is confirmed that this bleeding is Istihaadah (i.e. bleeding outside the monthly menses). So, the bleeding that comes during your regular time of menses is considered menses and whatever exceeds it is considered Istihaadah.
Besides, if you want to know that you are pure from menses, you may insert a piece of cotton and if it comes out clean without any blood or yellowness or muddy discharge on it, then you are pure.
In addition to this, the period of purity that is between the two bleedings is a valid period of purity during which you are obligated to perform the prayer and all other acts of worship.
Having known this, you would be able to determine whether these spots were menses or Istihaadah. If it is Istihaadah, then you are not required to do anything, and your Tawaaf and all your other acts of worship are valid, Allaah willing. But if it is menses, then your Tawaaf was not valid according to the view of the majority of the scholars; in which case, you must return to Makkah in order to perform Tawaaf and Sa’y because you are still in the state of Ihraam. For more benefit, please refer to Fataawa 89179 and 82627.
Nonetheless, some scholars are of the view that the Tawaaf of a woman in menses is valid but she has to slaughter a Badanah (a camel or a cow); for more benefit, please refer to Fatwa 115986. However, we do not see any obstacle to acting according to this view, especially if it is difficult to make up for this matter.
In any case, you are obligated to make up the prayers that you had performed without performing Ghusl during the interval between the two durations of bleeding if we presume that it (the bleeding) was menses, because a period of purity between two bleedings is a valid period of purity as we previously clarified. For more benefit, please refer to Fatwa 82827.
Allaah Knows best.