Hey Afro-Samurai
Restart your iPhone - Apple Support - See if restarting your iPhone resolves this issue. Restarting can refresh the iOS and can resolve strange issues like this.
If that doesn't help, you may want to provide some additional details about the issue.
Does this happen with links from all websites or just from YouTube?
Does this happen with links copied from any location? For example, only links from Safari, or are links pasted from other browsers or apps having the same behavior?
Does this occur with every contact you try to send a message to, or just one contact specifically?
Thanks!