If I use Mailgun with Laravel for a webform, who do I get my email account from, my DNS provider or my host provider?

I have a website setup using Laravel which uses a webform for visitors to send email to me. I use Mailgun as the driver. I have my domain registered with Namecheap. They said they are my DNS provider. I set up my website using Forge and DigitalOcean.

I have two email accounts with Namecheap's Private Email subscription. The instructions at Mailgun told me to change the setting from Private Email at Namecheap to use MX Records. When I did that I was able to get Mailgun working but I no longer could use the email accounts I had with Namecheap. Essentially what Namecheap is saying is that I can't have email addresses with my domain and use Mailgun at the same time. They said it is because I can't have both my email addresses and Mailgun configured on one domain. That can't be true.

What do I need to do to set up email addresses with my domain and use Mailgun as my email driver with Laravel?

via Chebli Mohamed