With my current headset mic my trumpet sounds kind of muted. I'm not really fond of music theory but I think what happens is that all the harmonics aren't captured.
As a result, I'm looking for a microphone! I don't need an expensive one, just 15-25 euros because as long as it's actually intended for (wind) instruments it's going to be a huge improvement.
I don't have any experience on this matter so I thought you guys might have some suggestions.
Greetings!

Hi! I'm not an expert but I got to learn some things about microphones through practice (and asking for advice), you can read some here: https://forum.jammr.net/topic/750/ (I guess if you search for “microphone” or “trumpet” on the forum you will learn more).

Yes, headset mics cut a lot of frequencies/harmonics. I guess the easiest/cheapest improvement would be to get a “standard” dynamic microphone (and a 1/4" to 3.5mm adapter for your computer mic-in socket, if that's not already bundled) and place it as close as you can to your trumpet.

The optimal solution would be one of those small microphones that can be mounted on your trumpet bell, but I guess they are more expensive, you should ask some music shop about them.

I hope we can have a jazz jam together some time!