I've been making tea at home forever. I used to use lipton tea bags. I'd brew the tea to my liking and just add sugar. I tried the baking soda thing and did not like the taste. If I put it in the fridge it turned cloudy and tasted bad. If I left it on the counter top it would stay clear and have good taste for 3 days. Never made it past 3 days.
About a month ago I started buying loose leaf tea at Teavana. Depending on what you buy it can cost more than lipton. But the flavors and quality of the tea are so worth it. Some teas, like white jasmine can be brewed more than once without loosing flavor.
With all of these teas I can keep it out or refridgerate and the taste stays good and does not go cloudy.
I also learned to brew the different types of tea at the correct temp. Amazing difference in taste quality.
I only add sugar and will never go back to grocery store tea.
Hope you get your tea sorted out.