  In this paper we consider the inhomogeneous nonlinear Schr\"odinger (INLS)
equation \begin{align}\label{inls} i \partial_t u +\Delta u +|x|^{-b}
|u|^{2\sigma}u = 0, \,\,\, x \in \mathbb{R}^N \end{align} with $N\geq 3$. We
focus on the intercritical case, where the scaling invariant Sobolev index
$s_c=\frac{N}{2}-\frac{2-b}{2\sigma}$ satisfies $0<s_c<1$. In a previous work,
for radial initial data in $\dot H^{s_c}\cap \dot H^1$, we prove the existence
of blow-up solutions and also a lower bound for the blow-up rate. Here we
extend these results to the non-radial case. We also prove an upper bound for
the blow-up rate and a concentration result for general finite time blow-up
solutions in $H^1$.
