Oh sweetheart I'm so sorry to hear that.

Basically no, you don't 'have' to have the D&C, if you are bleeding then your body should pass the bub. If the bleeding gets really heavy or prolonged or the cramping gets really bad, you should seek medical assistance though as your body might be having a bit of trouble on it's own.

I lost a bub after my first baby too, at 12 weeks. It never occurred to me that that might happen either. I'm currently losing another one and TBH even though this is my 3rd loss it still never occurred to me that it would happen. You have done nothing wrong.
I have had both natural m/c and D&C and neither was any easier or better to deal with IYKWIM? Your heart's loss isn't physical so I found that I was better able to deal with the whole situation on the inside when I felt more at ease and in control with my decision.

Good luck, and welcome to BB. There is lots of support and understanding here.