iPhone 5 wifi not connecting unless extremely close to router...?

I've had my iPhone 5 for about 6 months. I've never experienced any problems at all with it.

Over the last week, I've had major wifi problems. My phone only connects to my home wifi if I'm sitting next to the router, like a 7 foot radius from it. The minute I walk out of the room, it drops first to a low wifi signal, then shows the loading circle next to the wifi symbol, and then goes to either 3G or LTE.

The thing is, even when it goes to LTE or 3G, the signal is at the lowest bar as if there's no service at all.... sometimes, I'll have absolutely none.

There are 8 Apple devices in my family and every single one of them works perfectly with my home wifi no matter where I am in the house or in friend's houses with other home wifis...except mine!

I've never had this problem until recently so I'm not sure what triggered it.

Went to Verizon and they basically told me I was mistaken because it was working on their wifi (of course), so although I explained the situation, it was working while I was there, so they didn't believe me per say. They told me to call tech support if it kept happening and they did a soft reset on my phone. As soon as I got home, my wifi disappeared immediately and switched to low-service LTE.

I'm afraid if I go to the Apple store, it'll cost me to replace my phone OR they won't believe me or "fix" it, or they'll tell me some "easy fix" that actually doesn't work. Main problem is, I'm SURE their wifi will work on my phone so they won't be able to see what I mean when I say it's not working.

I've read of others with this problem and I've tried putting it on airplane mode, turning off, turning on, turning off airplane mode and turning on wifi. I've reset it. I've changed some wifi settings and done other random things but everything just works for about 3 minutes and then it goes right back to square one.

So... what should I do?

Thanks in advance-

Beth