Search for U-BLOX 4G.
Their modules often exist on a board which you can use more readily.
SMS is a basic GSM function, accessible over AT commands, and any such module should support it.
To get onto 4G or whatever, you send it ATDT*99# and that connects you to the network's internet and then your TCP/IP stack has to be connected to the module.
The problem in this business is that the chips or modules have a fairly short life so a design-in today may not be available in a few years' time. Currently I am using a U-BLOX GPS module (NEO-M9N) but that's a different thing. I used Siemens modems for SMS (TC35) but they dropped them, then Cinterion took over, then they dropped them, then somebody else took them over and then dropped them too. So a commercial email2sms service may be easier. But if you are developing a product to sell, people want it integrated so all you need to attach is an antenna.