Can I change the font in my messages

By default, you cannot.

You can download fonts from the App Store app , then use them in documents you create on iPhone.

1. After you download an app containing fonts from the App Store, open the app to install the fonts.
2. To manage installed fonts, go to Settings > General, then tap Fonts.

Install and manage fonts on iPhone - Apple Support (IN)

Tripletsplusone wrote:

How can I change the font in messages?

I don't think it is possible. You can only use downloaded fonts in apps that have a font menu.