How adding one more electron increases the ionization energy?
It's not just adding one more electron. Another proton is also added to the nucleus. The overall trend across a row is driven by shielding effects.

In general, as you go across a row, the shielding effect is fairly small compared to the effect of increasing nuclear charge.

As you note, there is a slight deviation in this trend between 5A (i.e., $\ce{N}$) and 6A (i.e., $\ce{O}$) because the extra electron in oxygen is paired. This increases the electron-electron repulsion, so the ionization energy decreases slightly.

As you note, $\ce{F}$ (7A) resumes the overall trend of increasing ionization energy driven by the attractive effects of the higher effective nuclear charge $Z_{eff}$.