I feel like cheating on my girlfriend?

[MM]

"is seeing each other once a week too much to ask?"

No, but it doesn't sound like you've actually asked that. You've asked her if everything's okay, you've let her know she can talk to you, but you haven't actually said, "Look, I know you've got a lot going on, but I'm feeling a little neglected. What can we do to fix that without putting too much of a burden on you? Can we maybe agree to make sure we see each other once a week, or text each other good night?"

If that doesn't work, then okay, time to move on. But move on. Don't line up the next girl before you're out of this relationship officially.