How to speed up phone without Factory Reset?

My phone has been acting a little slow lately. Mostly it is okay but one app it particularly slow. In Storage menu it says I have * total space of 24.12Gb * 649Mb available * 6.63Gb for apps * 1.65Gb of cached datay * 5.85Gb of Misc The app in question in App Info has * Total 859Mb * App 19.80Mb * Data 839Mb * Cache 37.93Mb The app also forces other apps out of memory (it seems) -- when I run the app, another apps that plays music seems to shut off and crash and I have to restart it. What app manufacturer told me: "fresh install is the best solution" (I understand it as delete the app, reinstall it, or maybe just reinstall it if that's possible). That means also that all my in-app messages (a lot of them) will be lost. What I want: Fast app, fast phone. What I am thinking: I am considering backing it up and doing a factory reset. I will lose basically everything. It's like getting a new phone. Question: what are some actions I can do to not lose everything and to speed up my apps again? Stuff I really want to keep are SMS + MMS, and I know that is possible. I also want to keep Viber messages, and other in-app messages, but I know it's probably not possible without rooting phone. Rooting my current LG G2 using various methods failed, so I gave up on that.