This article addresses a very common cause of the “can’t send mail from my iPhone” issue, and provides a very, very easy answer. Try this before doing the harder stuff.
There are at least a couple of reasons why you can’t send emails even though you can receive them. One reason, which is easy to fix, is that your iPhone has joined a WiFi network, and the iPhone is trying to send mail out through that network, and something about that network is blocking your mail. (Joining a network can happen without intervention from you, if the network doesn’t require a password– that’s an “open,” or “unsecured” network. You probably shouldn’t use an open network anyway.)
If the problem’s in the WiFi network just turn off WiFi and use your iPhone’s built-in cellular connection. You can do it via the Control Center (swipe up from below the bottom of the screen), or via the Settings app. Either way, just turn off WiFi, and see how it goes. If everything works when you’re not using the WiFi, you know there’s something about the network that’s messing things up. You’re not going to fix the network– that’s someone else’s job– so just don’t use it. Use your cellular service instead.
Note: the iPhone will always use WiFi if it’s available, even when it’s not working properly, and even if things would be better over the cellular system. You can’t tell the iPhone to prioritize cellular ahead of WiFi– if both are available, the iPhone uses WiFi. The only way to not use WiFi is to turn it off. Can’t hurt to try. You can always turn the WiFi back on later.
If you’re having the opposite problem (Mail works when on WiFi, not when on cellular) check out my article on that: How I Fixed an iPhone that Couldn’t Get Mail Unless On WiFi