1. FORGET everything they told you. If it was right you would already be playing above double C.
 

2. Work on some lip buzzing and the Stevens pencil exercise to build some lip muscle.

Buzz 15 - 30 minutes a day.

Put a pencil between your lips and push the lips together. The lips should hold the pencil straight out for 3-5 minutes a day.

The muscles that really start burning are the ones you use to play high. (NOT the same muscles as playing in or below the staff. First reason pedals are not the way to go.)

3. Work on soft playing. So soft that you almost can NOT hear it. That will help you learn to control a small lip aperture for playing high.

(The lip movement for the double high register are 1/64th as big as the lip movements in the pedal register. Pedals really slow down learning how to control the fine movements. Second reason not to do pedals.)

4. Project the notes where they belong.

Low G rolls out of the bell,
Low C goes out 5 feet,
Second line G goes out 8 feet,
3 space C goes out 12 feet,
G on top of the staff goes out 20 feet,
High C goes out 40 feet,
G above high C goes out 80 feet.

(Pedals are NOT to be projected like high notes. Third reason pedals are the opposite of what you need.)

5. Relax the stomach muscles. Tension only hurts the sound. Tensing the stomach muscles does NOT create a smaller body cavity or pressurize the lungs.

Bringing the abs in toward the spine and contracting the muscles around the girdle does create a smaller body cavity. That moves your guts and since the pelvic bones won't let them go down; they have to go up. That makes the part of your chest cavity available for your lungs smaller. And that places the air in the lungs under pressure.

Pull the stomach in farther for each higher note. (Not done with pedals. Fourth reason not to do them.)

6. Lip set point.

Take line 1 of page 125 in the Arban. It is a C Major scale with every other note jumping down to low G.

If you start on the Low G the middle c is hard for some players. If you set (and play) a middle c first and then start the high notes are easy.

I make my students do a 2 octave C scale. They set and play a G on top of the staff and withOUT resetting they start the exercise.

It is easy to compress the lips to play a half an octave higher than your set point. It is easy to learn to relax and (drop the jaw) to get to a full low g. That gives a range that will play the songs you listed.  The G on top of the Staff should ALWAYS be you starting point. That way you have a base from which to judge where every note is in relation to your starting aperture/tension level.

(Fifth reason against pedals. Opposite lip set point.)

The hit and miss embouchure (start on whatever the first note of the song is); keeps you constantly guessing where the notes are. If you have a 3 octave range then you use 36 starting apertures and tension levels. Where is the consistency in that?

Plus pedals use a different lip roll than high notes 6.  Pedals use a bigger jaw position and jaw movement 7.  Pedals need a huge amount of slow air not a little bit of fast air 8.

I CAN keep going but I think you see my point.

Information about my trumpet & embouchure books.
http://www.BbTrumpet.com
 
Best wishes
Clint 'Pops' McLaughlin