Emails form WordPress are not going though

I just switched my website over to a new domain. I also changed my email address. I am in Settings, trying to change my email address because I noticed my contact form emails on my website aren’t coming through to my email. In settings, WordPress says it sent a confirmation email to me, but I am not receiving it. No one at my hosting company seems to be able to assist me with this, as my email is set up properly and I am receiving everything outside of WordPress. Does anyone know how to fix this issue?