Who told you quick charge only works when the screen is off? Unless this is an S7 ONLY feature, that shouldn't be the case. Both our S5's & the wife's new Note 7 charge quickly while they are on and/or being used.
As mentioned, you can't gauge your SOT or overall battery life for that matter, off what others are posting online. We all use our devices differently, regardless of the similarity of apps being used.
I would suggest backing up all of your contacts, text messages, pertinent files/photos and do a factory data reset to see if that resolves your problem.
S5 tap'n