problem with iPhone 5s

Hi All,

I hope I'm putting this in the right forum, and I hope I can explain my problem so it's understood.

Earlier today I pressed the power button on my phone and voiceover told me what time it was, and then I hit my home button and heard the little bleep and voiceover told me what app was on the upper lefthand part of my screen and told me to double-tap to activate. Nothing happens if I double-tap the screen though, and if I press hard on the screen I can move from app to app but it won't do anything using the light touch that I normally use. Btw I do have one of the screen covers with the raised dots on it so I can tell where I am, but of course that shouldn't be causing a problem.

I called apple accessibility when I thought the screen wasn't responding at all but they couldn't help and told me to take the phone to what apparently doubles as our local apple store, but now that I'm able to get the phone to respond but with difficulty I thought I might ask here if there's anything I can do to avoid taking the phone for a possible repair, because it sounds like I may be without the phone for a while if it has to be sent off, and apple accessibility told me that I may even have to get a new phone but I've never set up ICloud to back up my apps and I'd rather not have to try to remember everything I've installed in the past year to put it back on a new phone if there's something I can still do with the phone I have now.

Oh I did try a reboot, but it was strange because I thought when I've done a reboot before that I had to power the phone back on myself, but this time it's been coming back on on its own without me having to do anything.

Also, when I was on the phone with apple accessibility the lady asked me to open settings, and I asked siri to do that and she did so it appears to be just my screen that isn't working correctly.