I've been playing trumpet for about 6 and a half years now (since 4th grade, currently in 11th grade) and I'm in my school's jazz band. I've had a Bach TR300 student trumpet for this long, and have never really found issues with it, but I recently thought that it is time I should probably upgrade. Any recommendations? Intermediate vs. Professional? Not too expensive.
Also, the highest note I can somewhat comfortably play is the D above the staff.

Sorry for having to wait so long for a reply!

There are many options from which you can choose to upgrade from your current horn. There are numerous considerations to be aware of when shopping for an intermediate to pro-level horns, e.g. bell/bore size, key of instrument, bell taper, thickness of material, gap size, etc. That doesn't even include choosing the right mouthpiece (but I'm assuming that's not an issue for you at the moment).

The best thing you can do right now in terms of upgrading is to go to a music store and try out horns. It is the only best way to get a feel for the horns your are most interested in. You wouldn't buy new shoes without trying them, right?

That said, most people look to upgrade to better horns that have a similar feel to their old horn, or in other words, takes the least time to acclimate. If price is an issue, consider looking into the Bach standard or professional line horns (the model 37 and the new commercial models), or even Eastman trumpets. Very similar feel to your current horn, and it won't break your bank. If price isn't too big of an issue, look into the Yamaha Xeno line or even Schilke. Both are much better in terms of quality of sound and physical composition, but are pricier than the Bach or Eastman. There are literally hundreds of trumpet makers to choose from and sometimes it can become overwhelming. But if you scale down your search in terms of price and familiarity, the search can become more manageable. Consider this website: http://www.dallasmusic.org/gearhead/New%20trumpet%20Guide.html

In terms of range, there are many ways to increase your range, but it mainly boils down to endurance, tightness of embouchure, and speed of air. You can practice lip slurs and long tones to develop those facets, but it will generally come with time. What's truly necessary is patience and a good work ethic. There are players who can play double Gs on the deepest of mouthpieces or the biggest of horns (i.e. flugelhorns), but they all have practiced to the point that they can play in that range without thinking or self-doubt/hesitation. On the other hand, it's also not absolutely necessary to have a super high range to get far in music as a hobby or even as a career, but having that knowledge in the first place is important nonetheless.

Good luck!