Oxidation states the elements in nitrosyl chloride

I have read that $\ce{NOCl}$ dissociates to $\ce{NO+}$ and $\ce{Cl-},$ and the various reasons stated as such seem fine.


But what I don't get is this: if we follow the actual rules of assigning oxidation numbers, we find that nitrogen has got an unit positive charge with an unit positive charge on chlorine too (if we follow the structure of $\ce{NOCl}$ closely).


So, am I wrong in judging the oxidation number of nitrogen in $\ce{NOCl}$ to be $+1$ instead of $+3,$ as the dissociation of $\ce{NOCl}$ seems to go against my interpretation? What should be the oxidation number of nitrogen in $\ce{NOCl}$ in that case?


