Hello, and welcome to TeenHelp!
Many people have strict or difficult parents, and they manage to stay in relationships. It sounds like your girlfriend broke up with you because she couldn't spend time with you outside of school. Maybe I'm not getting the full picture (there could have been other reasons why she broke up with you as well), but based on what you've shared, that's what I'm perceiving.
I know it's not ideal to be limited to "school time" when you're in a relationship... but after taking into account the lunch break (30 minutes?) and mutual extracurricular activities (e.g., joining the same after-school club), that might make staying in a relationship worth it. It's still SOME time Monday through Friday that you can be with your girlfriend. I know some people who are married to members of the military, so they'll go weeks or even MONTHS without seeing their partners. It's possible to maintain a connection when circumstances are less than ideal.
With regard to your father, you may want to check out these two articles on effective communication (
1) (
2). You may not be able to get everything you want, but with the right approach (e.g., calm voice, willingness to negotiate, respectfully asking for clarification), you may be able to spend SOME time with your girlfriend outside of the normal school schedule. At the very least, it can help improve your relationship with your father and build the foundation for better communication when the two of you have disagreements in the future.