No offense but grow some balls bro! You're a grown ass man and this girls not even your wife. I don't see why you need permission to do things. If my girl told me I'm not allowed to do something, that wasn't involving any sort of cheating of course, I would laugh at her.
Don't lie to her just tell her look this is what I'm doing, This is why I'm doing it, This is how I'll stay safe (bloodwork). She's not gonna dump you and if she does then she's not worth it.