Is the reaction involving a proton transfer a redox reaction?
Donation of a proton is not an indication of a redox reaction, rather an acid-base reaction (which may or may not be also involving a redox process). The only way to show the reduction/oxidation takes place is to demonstrate that the oxidation numbers do change:

$$
\begin{align}
\ce{\overset{+1}{H}_2\overset{-2}{S} (aq) + \overset{-3}{N}\overset{+1}{H}_3 (aq) &amp;→ \overset{-3}{N}\overset{+1}{H}_4+(aq) + \overset{+1}{H}\overset{-2}{S}^-(aq)}\tag{1}\\
\ce{\overset{0}{Pb}(s) + 2 \overset{+3}{Fe}\overset{-1}{Cl}_3 (aq) &amp;→ 2 \overset{+2}{Fe}\overset{-1}{Cl}_2 (aq) + \overset{+2}{Pb}\overset{-1}{Cl}_2 (aq)}\tag{2}
\end{align}
$$

As you can see, oxidation numbers only change in reaction (2), and are preserved in reaction (1).