On a bound on the chromatic number of almost planar graph

Let $G$ be a graph, which can be drawn on the plane such that any edge intersects at most one other edge. We prove, that the chromatic number of $G$ does not exceed 7. We also prove the bound $\chi(G)\leq\frac{9+\sqrt{17+64g}}2$ for a graph $G$, which can be drawn on the surface of genus $g$, such that any edge intersects at most one other edge.