As it seems you are exporting just a bunch of points. An idea would be to use a surface with a certain thinkness, here is an example:
sp = SphericalPlot3D[Abs@SphericalHarmonicY[3, 1, \[Theta], \[Phi]], {\[Theta], 0,
Pi}, {\[Phi], 0, 2 Pi}, PlotTheme -> "ThickSurface", PlotPoints -> 30];
Export["test.stl", sp]
