Hi
BestUnicorn ,
A lower score on your first official GMAT than on your practice test often comes down to test-day nerves, and that's very common. Since your target is 500 and you're already close based on your practice performance, I think reaching your goal by mid-September is definitely realistic.
My biggest suggestion is to thoroughly analyze your first official attempt. Figure out exactly where you lost points—whether it was timing, specific question types, careless mistakes, or anxiety. Some of those issues are much easier to fix than others, and focusing on them will give you the biggest improvement.
Since you're a student and on a budget, there are also several good low-cost (and even free) resources that can help. Feel free to send me a message if you'd like some recommendations.
Best of luck with your preparation—you've got enough time to make a solid improvement!