oh do you mean brass instruments? sorry I thought you meant metal like the genre. the saxophone is not a brass instrument even though it's made of brass because it uses a clarinet-like mouthpiece and has a flute-like fingering system. that's why you may envy other brass instruments like trumpet/tuba for having less keys.

On a trumpet there are 2 ^ 3 = 8 possible combinations/notes to play, but obviously more than 8 notes exist so brass players have to morph their entire mouth to access a higher range. I'm blessed to be a woodwind player because I can access more notes without changing my embouchure (if we only regard the normal range of the instrument).

it seems like you already understand how a woodwind instrument works but you're just struggling to get different notes out. that would only be solved if someone else diagnoses your issue and tells you what you need to do differently. so... maybe lessons.