Is first degree burn inside mouth an open wound and am I at risk to get HIV or STI in oral sex?

U R @ risk for STD. Wound or no woulds in the buccal mucosa; you are always at risk for std's; especially in today's promiscuous environment. The only way to ensure this would not happen is to have a very longterm relationship with an honorable partner who has been repeatedly tested negative; and whom you know is otherwise non-promiscuous by history. Although socially unpopular, best health is provided by celebacy.
More likely. Both open wounds will enhance the likelyhood. Anyone engaging in non-monogomous sex needs to have a partner use protection and be tested for stds.