I have represented standard deviation as "±SD" before in publications. But I like to have opinions on this. Is it appropriate to use the notation '±' with SD ? Or is it only for Standard error ?
Yes! you can represent standard deviation as "±SD".
For Example:- $\bar x\pm 2\times SD$, it just shows the lower and upper limit for most of individual output $x_i$ of Normal data. ($\mu ~rather~than~ \bar x$)
and, $\bar x\pm 2\times SE~of~mean$, shows lower and upper limit of population mean.