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Hey!

I know you said not to just say “tell them,” but remember secrets are hard to keep. I’m not saying to tell them right away or anything like that, but do know that it may be worse in the long run if they discover your secret instead of you telling them yourself.
But besides that, I think that if you’re not going to tell them you need to set boundaries with your partner for things that you and her can and can’t do when there’s the possibility of your parents finding out. For example if you’re on the phone with your girlfriend around your parents make sure she doesn’t speak as loud or doesn’t mention romantic things.
I’d also talk to your girlfriend to make sure she understands why you can’t do certain things like give her flowers more often or always have her around the house. Explain how you may feel about keeping the relationship a secret and what some of your worries are. At least then both of you are on the same page and have a mutual understanding.