There are lead pipes in Toronto. Get the water tested.
Also, take a look in your toilet tank and look for rust colouring. If it’s bad, it may be a concern.
Periodically, I think late spring and early fall, you might notice a musty door in the water. It’s considered safe to drink though.
Get yourself a zerowater filter and use it for your drinking water. Bed, Bath and a Beyond sells them. Change the filter when you notice the taste or smell. This will remove most things from your water, including the chlorine.
If the chlorine bothers you in a shower, get an in-line filter that screws onto your shower head like this one:
https://www.amazon.ca/gp/product/B07D9GCG5B/ref=ppx_yo_dt_b_search_asin_title?ie=UTF8&psc=1
I've gone through a number of showerhead filters and this one has been absolutely fantastic, I've purchased several as gifts as well and everyone can't live without it now. It's very affordable, comes with 2 filters and the replacement, 2 pack filters are under $20, plus they last a good long while. I very highly recommend it!
To answer your question about hair and the tap water here. The Tri-cities has some of the hardest water in the country. I've done a few PH tests and it's usually around 8.6. But that does fluctuate.
You can use a water softener, or don't wash your hair in tap water and instead use a reverse osmosis filter. Use that water instead.
You can also get an attachment for your showerhead. It installs in 3 minutes. This device softens the water as you use it. While not as good as an actual water softener, it does help. You can order it online from Amazon through that link, but they also sell them at Canadian Tire in the Brita Filter aisle and Home Depot somewhere. (don't remember)
Hope that helps.
Are you in an apartment or condo? I had this problem in my condo and this filter off Amazon did the trick. Just remember to flip the filter every month or two and replace it every few months: