NOTHING WORKS!!!

Since updating to iOS 9.3.5, my phone has more problems each day. Now I consistently have delays (sometimes hours) and failures in sending and receiving both iMessage and SMS text messages. Often when I do receive texts I get the same one multiple times. Searches on Safari are extremely slow and often fail. Connection to the internet is difficult to maintain. Most recently I cannot answer phone calls. I have an iPhone 6 that is a little less than 2 years old. There does not appear to be a carrier update available. I have reset the network settings. I have done multiple hard phone resets. These issues are not affected by whether I am on home internet versus another internet source, and likewise are not affected by whether I am on data versus internet. Does anyone have any idea what could be wrong or what I can try next? Thanks!