The pH of human skin is normally acidic at a pH of around 5.4 to 5.9 (see
this link and
this link) so having the pool be unusually acidic isn't likely to cause a problem to skin unless it's much more acidic, such as in pools that use Trichlor without adjustment that get down to a pH of 4.5 or lower (i.e. they immediately show red on the TA test). Generally, it takes a fairly low pH below 3 to cause itching -- lemon juice is around a pH of 2.3 and if put on your skin and left to dry you will probably find that it itches.
Alkaline soap has a pH around 9-10 but can feel slippery on skin rinsed in soft water as some of the soap remains on the skin. If the pH is higher, such as found with lye (13 or higher) or undiluted bleach (11.9 or higher) or chlorinating liquid (12.5 or higher), the oils in your skin saponify which basically turns fats and oils in your skin to soap which is why it feels slippery.
So generally speaking, a pH range of 7.2 to 8.2 isn't going to do very much with your skin unless you have very unusual sensitivities. Tap water is usually in the pH range of 7.5 to 8.0 (yours is 8.1) and is intentionally made more alkaline than neutral in order to reduce metal corrosion.
Your eyes, on the other hand, are more sensitive to pH changes in the water, but still not that sensitive at least to pH. The pH of human tears varies somewhat but averages 7.5 (see
this link while
this one says the average is 7.0[END-EDIT]).
This paper talks about various factors affecting eye irritation in swimming pools. The primary factor for irritation appeared to be osmotic pressure since adding salt to the water at around 0.5% (around 5000 ppm) in the field study or 0.7% (around 7000 ppm) in the lab study virtually eliminated the irritation which isn't much of a surprise since the salinity of human tears is around 9000 ppm. The pH varying from 7 to 9 did not show a significant difference in irritation. A 1975 paper by Eichelsdoerfer, which I can't find, describes how the chloramines can be more irritating. Other studies show that nitrogen trichloride (see
this link among many others) can be particularly irritating. PH below 7.2 causes many people to feel some rather mild stinging of their eyes and PH in the low 6s or lower can result in some skin itching and somewhat worse stinging of your eyes.
When there is no CYA in the water, then the production of volatile and irritating nitrogen trichloride is much more prevalent, especially with higher bather (or other organic) loads. Also, it is very dependent on the pH where far more is produced at lower pH (from a pH of 8.0 to 7.0 and with no CYA the amount of nitrogen trichloride increases by a factor of 4.3 whereas the active chlorine level increased by a factor of 3.4). So I strongly suspect that the main correlation with eye irritation as well as "bad pool chlorine" smell, coughing and other problems is mostly associated with nitrogen trichloride and that at lower pH more is produced. It isn't the pH of the water itself that is the problem, but rather the effects on the chemistry of what is produced at the lower pH.
In pools with CYA in the water, especially in residential pools that typically have low bather load, I suspect that preventing moderate changes in the pH are more important for protection of plaster surfaces and to prevent metal corrosion than for prevention of irritation of the human body.
(Full cite on Eichelsdoerfer paper: Eichelsdoerfer, D., Slovak, J., Dirnagl, K., Schmid, K., 1975. Irritant effect (conjunctivitis) of chlorine and chloramines in swimming pool water. Vom Wasser, 45, 17-28 (translated).