Jefferson, I also play Seydel Blues Session harps (amongst others) and find them to be some of the most comfortable harps I own. Is your harp actually tearing your lip, as in causing a laceration of the tissue and drawing blood? If so, SEND IT BACK to Seydel with a note explaining what's happening and at which hole(s), blow or draw. I'm betting if there's a problem with the harp they'll send you a replacement very quickly. (They have exceptional cusomer service.)
On the other had, if your lips and mouth are just sore, particularly if you're using the "pucker" method, that will pass soon.
Lip balm is usually pretty safe. With proper embouchure (the way you hold the harp in your mouth and how you hold your mouth/tongue/throat/nasal cavity) it shouldn't get into the harp. Your embouchure should have your mouth open enough that your top and bottom lips are well onto the harp
covers, not puckered up tight against the holes. Be sure to give yourself a break now and then, too.
Welcome to the Forum, and welcome to the harp!