Hello meaganthomson,
We would like to see how we can help you with your mail accounts not syncing between devices. Have you tried deleting the account from your iPhone and then adding it back? If not, please try so and get back to us with your results. To delete an email account go to Settings > Mail > Accounts > [Email Account] > Delete Account. Then follow the steps in this link to add it back: Add an email account to your iPhone, iPad, or iPod touch - Apple Support
"Set up automatically if you use a common email provider
If you use an email provider like iCloud, Google, Microsoft Exchange, or Yahoo, Mail can automatically set up your email account with just your email address and password. Here's how:
- Go to Settings > Mail, then tap Accounts.

2.Tap Add Account, then select your email provider.
3.Enter your email address and password.
4.If you see Next, tap Next and wait for Mail to verify your account.
5.If you see Save, tap Save."
Cheers!