Is it normal to want to starve but end up eating the next day?

Not normal. That's one of the worst methods to lose weight, and you damage your health without even obtaining results. Don't cheat. Take it the hard way, it's a lot better. Hit the gym, get a training schedule. Change your eating habits, especially the types of foods, but don't starve yourself. Your body will instead react abnormally if you do, will start storing more fat for periods like that when you don't provide food, and you end up in a worse condition. You try an abnormal thing and you will end up with abnormal and unexpected results. But you want normal and expected results, so try normal things, like we all have to do, exercise a lot and have a healthy diet. I suggest trying to get it from experts.

Edit: Your BMI says that you have a healthy weight. You should NOT become underweight, because that is abnormal, and abnormality leads to problems. You should NOT be concerned with your weight anymore. You should instead consider healthy nutrition and exercise, but NOT sprcifically for losing weight. Again, you are "very" normal, and you might not realise how many people struggle to stay in the area of normality, while you try to get out of it due to concerns that exist only in your mind. That's bad and you will regret it one day.

You're gonna mess up your metabolism.

Starving yourself is not a good way to lose weight. It can even train your body to store more fat. Please do yourself a favor and do some research.

As DDaviDD has said, it's bad and not normal.
What you are saying could easily derive in a full anorexia or bulimia. What I recommend it's doing nothing and accept yourself like you are. You are healthy, you don't need to do anything, so don't do it until you accept yourself. If not, you could be risking your health with things like Muscle dysmorphia.

I get horney when I think of starving myself tbh. But yes I eat every few days.

I'm 5'9 106lbs