You ask whether there’s effect on your pH level from swimming several times a week in a chlorinated pool and whether inserting a tampon would provide some protection. The vagina is, in its natural state, not an open space but collapsed, that is, the walls are lying next to each other. Imagine a balloon before it is blown up. We refer to the vagina as a “potential space,” because space is made there only when needed—for a tampon, childbirth, or sex.
The vaginal pH isn’t disrupted with a relatively brief swim or tub bath. Inserting a tampon actually would be more likely to act as a wick, introducing more chlorinated water because of its absorbency.
Chlorinated water certainly can affect the vulva and surrounding skin; I do hear that from a number of patients. In that case, be sure to rinse thoroughly after swimming, and then apply a product like Lubrigyn Lotion (available in wipes, which you can put in your bag to take to the pool) to soothe by moisturizing.