Hello rgg_rgg,
Ensuring your sent emails appear in the Sent folder is important. Since having this issue have you confirmed the email appears in the Sent folder via the email providers website? If not, this is a great step that can help isolate the issue. If the email appears in the Sent folder via the website, the next step would be to restart your iPhone. While simple, restarting is a great step that can help with resolving many issues. You can find the steps for restarting listed below and outlined in the following article.
- "Press and hold either volume button and the side button until the power-off slider appears.
- Drag the slider, then wait 30 seconds for your device to turn off. If your device is frozen or unresponsive, force restart your device.
- To turn your device back on, press and hold the side button (on the right side of your iPhone) until you see the Apple logo."
Restart your iPhone - Apple Support
Let us know how that goes!