organic chemistry - Why is o-fluorophenol a stronger acid than p-fluorophenol?

The $\mathrm{p}K_\mathrm{a}$ value of o-fluorophenol is $8.7$, while that of the p-fluorophenol is $9.9$. It's obvious that the inductive effect is more dominant at ortho-position, which results in a more acidic nature.

However, won't the $\ce{H}$ attached to $\ce{O}$ form a hydrogen bond with the $\ce{F}$ at ortho-position resulting in a less acidic nature than p-fluorophenol?