Authentication matters more than the address, and should be correct either way.
SPF
Lists which servers may send for your domain. With a dedicated IP you can name that address specifically, which is more precise than a broad include.
Check and repair it under cPanel > Email Deliverability, or add the record manually if your DNS is hosted elsewhere.
DKIM
Cryptographically signs your messages. It is unaffected by the IP address and should be enabled regardless.
DMARC
Tells receivers what to do when SPF or DKIM fails, and where to send reports. Add a TXT record named _dmarc, starting with p=none to collect reports, then tightening to quarantine and reject once your legitimate sources all pass.
WITH A DEDICATED IP SPECIFICALLY
Also request reverse DNS matching your mail hostname, and ensure the forward record agrees.
THE ORDER OF WORK
Get authentication right first. Most deliverability problems are authentication problems, not address problems, and a dedicated IP without correct SPF and DKIM performs worse than a shared one with them.
