In most similar instruments, the squeaks usually are caused by a tiny bit of leakage at one of the keys/pads/fingerholes. On some "padded" instruments pressing too hard may produce unexpected leaks on some keypads, but it's usually from letting off the finger pressure on one or another key while you're concentrationg on another problem. On unpadded holes, "squeezing down" when you concentrate on something sometimes may cause you to "roll the finger pad" a little off the hole.

Poor tone and inability to produce some notes is likely to be due to a mismatch between the "mouth tuning" and the instrument tuning. Ideally, the "backing cavity resonant pitch" of your mouth and throat needs to be close to the resonance of the instrument at the pitch you have fingered. A "mismatch" causes the "node" at the entry to the sounding part of the instrument to "wobble in and out" of the hole (or the reed cavity on other instruments), affecting both the stability and the tonal quality of the note sounded.

A good practice excercise is to blow - without the flute - so that the pitch you "think" is present in the air stream. It doesn't have to "whistle" but even a free flow will have a "pitch" that's discernable if you're producing a "clean flow." Practice "running up and down scales" to try to feel how you're adjusting your headbones (mostly tongue for most people and for high notes, but throat "tension" changes can affect lower pitches) as you change the pitch.

When you have a "sense" of how to "make the pitch in your mouth" applying the same tuning with correct embouchure and "into the flute" may give you a better control and tone.

For the higher notes on a flute, you may have to squeeze down the mouth volume to fairly tiny sizes. where stability of the flow can be more difficult to control, but for most people the notes in the flute range are achievable with a little (always a little more)practice.

I have met a couple who confessed that they just had "too big a mouth" to be successful with certain instruments, but that's probably not your problem(???) ;>) (?). (And the ones who made that claim probably were just too busy yapping all the time about how hard it was to really practice seriously.)

The usual advice to "blow harder" to get the high notes is technically incorrect, but works sometimes because when you try to blow harder you instinctively "tighten up" the mouth so that you may accidentally "tune up" to the note. It does, on many instruments, require a slightly higher air velocity for stable high notes than for low notes (which may need more air volume), but you have more control over the velocity by "making a smaller hole to blow through," sometimes with a very little more pressure, than by concentrating on cranking up the pressure and blowing the top of your head off.

Many people who play quite well do a lot of things "right" by accident. For some that seems to be the only way they can learn(?). No need to argue with what works; but "being in tune with the instrument" is probably the most basic thing that really helps with most wind instruments, and that's really hard to learn through anything other than lots of practice.

John