am i giving my bf thrush

i’m kind of embarrassed to be writing this but for the last year i’ve been in a relationship with a guy who gives me a lot of head. just in the last few months he’s had these red dry patches around his mouth which i thought was just sensitive skin but the patches have cleared up a lot over the last week which i mentioned to him and he told me he thinks it’s because he’s been using thrush cream and it’s helped. i could tell he was wary of me being embarrassed and told me it’s probably because he bites his nails, and that’s if it is even actually thrush. i’ve had a yeast infection before and i have had literally no symptoms the whole time we’ve been together but is it possible i’m giving him oral thrush from him giving me head??