Change in pH when boiling off acidic water
$\rm H^+$ ions (as well as any other ions, for that matter) do not boil off. Acid does. Depending on the nature of the acid, it might boil off faster or slower than water, and hence your pH might shift up or down.

$\ce{HCl}$, in particular, forms a high-boiling azeotrope with water at 22%, so the solution of pH 2 (which is pretty dilute) would form a vapor enriched with water, and the liquid phase would get enriched with acid. So despite the seemingly volatile nature of $\ce{HCl}$, it will mostly stay in the solution and make it progressively more acidic as it boils.