Here is a modification that works (note that I changed your argument to data from points):
Show[ListPlot[data],
Graphics[Text[#[[2]], #[[1]] + {0, 0.05}] & /@
Transpose@{data, labels}]]
and here is a version without needing to use Show:
ListPlot[data,
Epilog -> (Text[#[[2]], #[[1]] + {0, 0.05}] & /@
Transpose@{data, labels})]
