a) Firstly check in Textra Settings > MMS if you have a 'Manually Configure APN' setting, ensure it's NOT ticked. This means Textra was able to ascertain your APN settings correctly from your existing device settings, so 99% likely these are correct.
b) If you don't have this (Manually Configure APN) setting, locate the details as below and enter them into Textra.
* contact your carrier and request the correct MMS APN settings for your device; or
* check in Settings App > (More...) > Mobile Networks > Access Point Names (MMS)
c) Some carriers only support a 'Carrier Send Limit' of 300KB (Textra Settings > MMS). So first set the size to 300KB to see if that helps when sending.
Once you have checked these details, please send yourself a test MMS.
If still an issue, please send us a screenshot of the Textra Settings > MMS page along with what happened when you sent yourself a test MMS as instructed above.
If you can send MMS perfectly but keep getting the 'Check APN...' notification when receiving an MMS then it's certainly another SMS app (even if not the default one!) interfering, uninstall it, clear the notification and test by sending yourself an MMS. Check in the stock app to ensure MMS > Auto-Retrieve is OFF