More work on long tones in the low/mid register will be a big help. To strengthen the embouchure and give your upper-register something solid to work from.
Focus on getting a good, centered sound and playing in tune. Building upwards as your middle-register extends higher.
You can't play every day? It's tough when you can't devote yourself to playing more... 5-10, 2-5 minutes.... it'll take a little more time than that. You're working on an anaerobic exercise, which will take time for the muscles to adapt to what you're making them do. I try and spend about a half hour just on the
first exercise for a warm-up.