Am I in danger using this lithium polymer 3S 11.1V battery?
The 11.1V or 3.7V per cell is the nominal voltage. It will be less when drained, and more when fully charged.
A fully charged cell should be about 4.2V per cell or 12.6V.
The battery voltage is not too high.
But we cannot know if it has had any damage that would make it simply lose some capacity or if it has also become dangerous if it was overdischarged to 8V, or 2.67V per cell.