It sounds like your webhost is using “shared hosting” where many different clients are hosted on the same server. This is common for economy hosting plans, or sites that don’t need to handle enormous amounts of traffic.
Solution: As shared hosting isn’t the best for sending e-mail, we highly recommend trying a plugin like the WP Mail SMTP to offload the mail sending to a third party provider like SparkPost (or Gmail).
Once you offload the sending of emails from your webhost to a dedicated mail server, those emails should start getting out 🙂
Here’s a quick video we have about this common problem: