Actually, I'm sure you believe in more than this because the Mosaic Law was only instituted in 1445 BC - and there was a longer period of time before that than there has been since with two dispensations (BC/AD to use your terminology).
So, there was at least something going on between the Fall and the Law. So that is 3 dispensations.
There was a major change that happened at the Fall, so the pre-Fall era marks a 4th dispensation.
And if you're not an amillennialist, then you believe there is an era in God's program after Christ's return that is different than anything that has preceded it - so that is 5 dispensations.
So, you are definitely a dispensationalist in your overall view of history - and the only two additional dispensations I see are between the Flood and Abraham and between Abraham and the Law. The reason for a different dispensation from Abraham is because Israel didn't exist until that time - which I assume you would agree with - and if so, that takes you to six.
Also, there was a major change after the Flood with the Noahic covenant - a basic form of human government was instituted with the introduction of capital punishment, the eating of meat was allowed, a promise of no more judgment by flood, etc. So, this is all 7.
Beyond that, the covenants you mentioned are biblical covenants, which also provide part of the framework of dispensational theology - as opposed to the theological covenants of Covenant theology - so, it seems that you're far more dispensational in your thinking / theology than you realize.