iPhone 5S not receiving text messages, but still getting iMessages

On Wednesday evening my iPhone 5S stopped receiving text messages. Eventually, it would pick them up all at once, but then would go back to being unable to get them. When I looked up the problem, I followed all the steps, including updating the iOS (I am now on the latest one, whereas before I was on 7). It was pretty okay for a while, but whenever I plug it in to charge I stop receiving texts again. Late last night I charged it, and expected all my texts to come in by morning. This, unfortunately, has not been the case. It's noon and my texts still have not come in. Luckily, all my friends have iPhones, so I can still iMessage them, but my boyfriend has an Android, and I rely on texts to communicate with him.

Just a side story, last year with my iPhone 4S I went on a trip to Florida and halfway through it stopped picking up wifi, was overheating and dying within an hour of having charged it to 100%. This year I went to Florida again, the same resort, and my new phone was fine, but the Wednesday I came back it stopped receiving texts, as I said above. Is this just a coincidence?

Anyway, if anybody has any solutions to getting my phone to get text messages again, it would be greatly appreciated.