Network service

I have been having continous problems since last week with network service. Sometimes i simply can't make or receive calls or texts, other times my phone says I have no network service at all. I've done the turning my phone off/on, cleared cache in my apps, etc. I spent a good deal of time on chat with customer service and he suggested I get a new SIM card. I got the new SIM card and my phone worked OK for a couple of days, but then it started having the same problems. Last night with the severe weather in my area I couldn't make and calls or texts which was quite concerning since I don't have a home phone. Today the ordeal continues, but dropped calls are now occurring. I pay too much on AT&T services for these problems. There are other companies I can go to.