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.
Well it's possible only if you are deleting unnecessary apps and free us the storage. Another thing that you can do is root your phone and delete even those system apps which you don't need. 

But I prefer to factory reset the phone to speed it up.