If you can't deliver mail to Yahoo or Gmail, or to mailboxes hosted behind Proofpoint or Mimecast, you've got a deliverability issue.
But if you can't deliver mail to yourself, you've probably got a whitelisting (allow listing) issue, and not a deliverability issue.
What I mean by that is this....when you're sending "to yourself, from yourself" using your own domain or sub-domain in the from address, and you're sending to your own corporate mailboxes from an external email platform like an email service provider, some corporate anti-spam or security filtering is going to be extra suspicious of this. The filtering system expects the mail to be coming from inside the corporate network. It doesn't usually expect it to be coming in from an external source. Even if that mail is authenticated properly with a DKIM signature and SPF authentication in place, it can end up blocked, falsely perceived to be phishing or spoofing.
In that case, the fix is to configure your anti-spam system to "allow list" (whitelist, or exempt from certain filtering) this mail based on whatever identifier is appropriate: Sending IP address if your external sends are coming from a single IP address, or via DKIM authenticated from domain, or via SPF authenticated bounce domain. (Be careful not to be overly broad in whitelisting. You only want to allow good mail through, not mail that spoofs or fakes your email domain.)
The fix, most of the time, is not going to involve changing some setting in your other email sending platform or ESP/vendor partner's system. If mail from that system is passing all authentication checks, and is getting delivered successfully to other companies and to most ISPs, then there's no platform issue. No deliverability issue, no reputation issue.
That's a common thing for senders to get confused about. Yes, there are scenarios where you might need to change what you send and who you send it to, or scenarios that might reveal a misconfiguration of a sending platform. But this usually isn't one of them.