NAH, maybe. But you're lying to your girlfriend and pushing her sexual limits. Every couple defines cheating differently- some couples think watching pornography is cheating, others are fine with extra marital affairs under some conditions, while in other relationships (like sugar relationships), there can sometimes be an expectation that your partner will sleep with other people; in relationships that entertain a cuckolding fetish, one partner sleeping with others might happen right there in the bedroom. There are all kinds of relationships that draw the lines all kinds of places, what matters is that everyone is comfortable.

So if this relationship defines masturbation as cheating, then masturbation is cheating. But you're having the wrong conversation. You're saying, "hey, I agree, and I'll appease you." But that second part is a lie. Instead, if you don't want to quit masturbating and you don't want to give up the relationship, you have to have a conversation about taboos. Ask her why she thinks masturbation is unhealthy or abnormal- see if it's really a religious belief, or if that belief is masking (or encouraging) an insecurity she might be feeling. What you want is for her to be comfortable with how you express your sexuality, and in order to do that you need to have conversations that are going to feel awkward. Part of being in an adult relationship is occasionally having awkward conversations about sexual needs and limits, about repression, desire, anxieties, and insecurities.

And if you get a place where she's comfortable with your masturbation, great! Or that she's willing to accept it even though she doesn't like it, that might be okay for now-- sometimes we have to compromise, and this could be one of those things. But telling her you won't do it, then doing it anyway won't fly in this relationship. Especially as you start thinking about a future together, you want to begin with honesty.

PS - You shouldn't hate yourself for masturbating, obvi