Calibration Curve Error Propagation
I will try to offer a detailed way to propagate errors here, but before beginning it's worth asking what your audience is likely to expect "error bars" to mean.  In your field are error bars usually determined simply by replicate analyses of the same sample?  Or replicate samples of the same experiment or field site?  If so, it's probably best just to stick with what your audience is likely to expect.  That said...


The theoretical best way to fit your calibration curve would be with weighted linear least-squares algorithms.  In that algorithm, in addition to the {x, y} data, which in your case is $\{\ce{Sr_{known}, Sr_{meas}}\}$, you also supply weights corresponding to the uncertainty in the y values.  The weight for each y data point would be $\frac{1}{\sigma^2}$, which you could calculate from the $2\sigma$ uncertainty given by your instrumentation for that data point.  In practice, if you did this, I doubt that the parameters of your calibration would change very much at all from what you did previously.  But formally the weighted variant of least-squares is required if the uncertainty in y depends on y.  See wikipedia for more.
After doing the (weighted) least squares calibration regression, you can find the uncertainty in the estimation using the calibration equation.  $\sigma_{est} = \sqrt{\frac{\sum{\left(y_{pred}-y_{meas} \right)^2}}{N}}$.  In that equation $y_{pred}$ is the calibration-predicted Sr concentration and $y_{meas}$ is the measured Sr concentration, and for you $N$, the number of data points, is 37.  This uncertainty is one part of the uncertainty you'll eventually report, and reflects the uncertainty in your calibration curve.  Based on the R-squared you reported, my guess is that this uncertainty will be low.
After all that (!), you need to estimate the other major source of uncertainty, the uncertainty in the measurement of your unknowns ($\sigma_{meas}$).  There are several OK methods for doing this, the best of which would be replicate analysis of several samples.  It might be OK to use the $1\sigma$ value calculated from the $2\sigma$ uncertainty reported by your instrument too.
Finally, combine the uncertainties with the standard equation for combining multiple sources of uncertainty $\sigma_{total} = \sqrt{(\sigma_{meas})^2 + (\sigma_{est})^2}$.