Have you tried a different SMS app?
One thing that isn't completely clear: you say that the problem started after an update to Nougat, you say that you are out of your home country, and you say that SMS sending worked on your home network. So did you send any messages from your home network after updating to Nougat? If so it's most likely a problem with your account/home network/roaming network rather than the phone. Only if you had sent roaming SMS on this trip before upgrading to Nougat can we be fairly sure it is the upgrade rather than the roaming that's the problem. Even then, have you tried switching to a different roaming network, just to be sure it's not a problem with a particular local network?
I don't have an answer, just thinking about how I'd eliminate variables. Though if you upgraded while abroad you wouldn't know whether you could send SMS at home, so we can't eliminate them all just yet. SMS is a really basic part of the GSM standard, so doesn't need anything special enabled on the phone (unlike MMS, where APN settings are important) - the only control you have there is choosing the default messaging app.
I've not found other reports of problems like this, so can't rule out it being something to do with your account rather than the update. It might be worth contacting your carrier if it isn't fixed by selecting a different roaming network or using a different SMS app.
