Actually, I suggest using a dechlorinator that also eliminates chloramine (bonded chlorine and ammonia), and heavy metals (that can exist in most non RO/filtered water).
I use StressCoat (1 mL per gallon), I have since I bought my betta over a year ago. The aloe in it doesn't seem to affect the labyrinth at all in my experience. I have always had mine in at least a 10 gallon tank, so it has never been too strong.
If you have a smaller tank for your betta, there is products, usually by the bettas that is not so strong, as in a few drops per gallon.
It really is a very important thing to eliminate chlorine/chloramine. It is deadly to any fish. Just think about drinking pool water, or inhaling bleach powder, since that is kind of what it relates to. It also takes away their protective slime coat and then starts to burn them.
Also, keep changing the water regularly, as ammonia and nitrite are not good for bettas either. Don't know what kind of tank you have, since some of the smaller tanks do come with filters, which is a very good thing for the fish.
On another note, if you can verify that your water system uses chlorine, then you can let the water sit for 24-36 hours and the chlorine will dissipate. The problem is, if your water system uses chloramine, then it will not dissipate and be just as strong as when you set the water out.
For getting the correct temperature, you can go to a restaurant supply store and pick up one of their meat thermometors (used to make sure the inside of the meat reaches the proper safe temp). Using this takes all the guess work out, you can get an accurate reading of your tank temperature, then adjust the tap to the right setting. Otherwise, use the soft part of your hand and inside of your wrist to try to best match the temperature as you can.
Clean, toxic-free water at the correct temperature (78-82F) will slowly bring your betta around to a happy bubble-nest making bratty boy.
When you said both tanks, did you mean a second betta tank, or a tank with a different kind of fish? Shouldn't matter much, since they both need dechlorinated water, but I could suggest if the other tank is bigger, get the stronger dechlor, and if you know someone who is diabetic, get a syringe from them and 1 mL isn't so hard to measure
Just make sure to shake the dechlor well before hand, as it makes it consistent throughout the use of the bottle.
Hope your betta is feeling better soon.