Jen,
We have three earthquakes recorded in the general vicinity of New Madrid
during the years before 1811. These occurred as follows:

Dec 25, 1699 - an earthquake of Intensity IV was felt south of the New Madrid area
That's enough to feel the shaking and to cause loose objects to swing.

April 4, 1792 - an earthquake was felt in the region Northeast of New Madrid.

Jan 1, 1795 - an earthquake with intensity V was felt in southern Illinois.

That is about all I have. The area was not well populated and small earthquakes
had to be noted in diarys or logbooks - that didn't happen unless it was
an especially notable event. It is quite likely that small earthquakes were
happening, but went unnoticed.