Question on replacing iphone...

My phone recently died and won't respond to anything. I thought it may have been my charger but i tried it with other chargers, so it must be the phone. What was weird was that when I tried to charge it for the last few times before it died, there was a different symbol, one that i've never seen before, where the little lightning bolt usually is. But, my main question is, once I get a new phone (i have insurance and am going to the verizon store tomorrow) will the texts, snapchats, etc.. that I missed while the phone was dead be there?

thanks