I remember a bit of this in undergrad gen chem. If pH stands for -log([H+]), how can pure water (H2O) have a pH of 7? In theory, there shouldn't be any hydrogen ions in pure water. Turns out there are two simplifications being made: i. H+ in aqueous solution is synonymous with hydronium ion (H3O+). ii. Water is in an equilibrium autoionization reaction with itself and the hydronium and hydroxide ions: 2H2O H3O+ + OH-…
The stoichiometry which factors into the definition of pH is
H_{2}O H^{+} + OH^{-}
which actually includes the activity of proton - that's H^{+} multiplied by a coefficient that reflects the ionic strength of the solution and in non-zero outside of really pure 18 mega-ohm RO water - but that's beyond the scope of this. I will note that your balanced equation is in fact valid, as it includes bulk aqueous water.(1) H^{+}(aq) is not synonymous with H_{3}O^{+}; the former is aqueous solvated proton, the latter is hydronium ion;
(2) Moving on to the so-called "autoionization" reaction, what you mean to say is that water is self-ionizable or, more appropriately, amphoteric, i.e., is can act as an acid (in this sense, a proton donor) or a base (the hydroxide ion);
(3) The pH of 7 is an ideal and is dependent on temperature, ionic strength, and a few other things (including pressure) that do actually move us off the pH point of 7 for a so-called "neutral" solution; and finally
(4) The units are moles per liter; and hydronium vs. proton does make a difference, as proton is one hydrogen and hydronium is 3 hydrogens.