could i really be ovulating?

I gave birth just a week ago. I was just a little over 20 weeks. We were cleared to try again. I know it's unusual to ovulate this soon but i only bled for 2 days, now im having very dark brown spotting that the doctor said you usually have right before your first postpartum period. 
I have been taking pregnancy tests daily and they are extremely faint now. I took a digital ovulation test and got a positive. I know none of you are doctors, im just curious on others opinions. 
I know ovulation tests can pick up pregnant horomones but would it be positive since the pregnancy tests are extremely faint?