That doesn't mean you must allow for negative number of flowers. Heck you should be able to reason that just because the sd is greater than the mean doesn't directly imply that there must be negative values. Just play around with the parameters of a gamma distribution - you should easily be able to find some combinations that result in a standard deviation greater than the mean.

When in doubt simulation to verify answers isn't a bad approach either. If you know R here is some code to simulate your situation...

Which is close enough to what you got.

Also keep in mind that the standard deviation is more sensitive to outliers/skew than the mean is. For example here is what happens if we add a single outlier to some N(1,1) data...

The mean increased by approximately 100 and the standard deviation increased by approximately 3160.

P.S. You don't need to worry about how you're posting. You did a great job with formulating your question and showing the work you've done to get there.