Is it normal to be obsessed with your girlfriend?
If you mean you’re really into your girlfriend and think about her a lot, that’s pretty normal. If “obsessed” means you’re monitoring her, feeling unable to function without her, or ignoring her boundaries, that’s worth taking seriously.
People often use “obsessed” to mean head-over-heels, especially in a new relationship. Wanting lots of time together and thinking about your girlfriend a bunch can be part of being excited about someone.
The important difference is whether the intensity still leaves room for both of you to have your own lives. Constant checking up on her, trying to control who she sees, or feeling panicked when she’s unavailable can put pressure on the relationship. Give each other space and talk honestly about what you’re feeling—without making her responsible for managing all of it.