An answer I gave recently to a similar question
Squeaks happen for a number of reasons. It is hard to diagnose without seeing and hearing your sister play. But here are some things based on what i see daily.
1) Bad or Tight embouchure
Squeaks happen when your mouth is too tight around the reed. The reed gets restricted and hence can't produce a sound. Your mouth should be tight ( as in a tight seal around the mouth piece) but with NO tension, with a firm chin.
2) Damaged reed
If your reed is chipped or damaged this can also produce squeaks. Then it is simply a case of breaking in a new reed.
3) Fingers not covering the holes
This is a common one especially in beginners when they first try the second register. From your question it sounds like this is the most probable cause. Practice slow leaps from the low note to the high note i.e just putting the register key on. Most clarinet books have an exercises like this in their pages. Slow practice yes but useful first step in getting your fingers down covering the holes and the register key on at the same time. Often in this case fingers are later/earlier then the register key (as in a millisecond later) and hence a squeak happens. Look down or use a mirror and watch your fingers as they go down. Most likely if there is a millimetre gap , ie.e your fingers don't land exactly on the hole, a squeak happens. You may also want to check that you are keeping your fingers close to the keys. Check that in the mirror too. Far out fingers create late notes too.
4) Pads
You may have a damaged pad or too. damages pads create openings in the holes and unwanted notes. This is less likely though, if the low notes are working then it is less likely that the pads are damaged.
5) Breathing/ breath support
Remember high notes need breath support and more 'push' then low notes. If you don't know what breath support is then google it or ask your clarinet teacher to show you some exercises. Too much air can also create squeaks use your breath support rather then your air to support the note.
6) Fingering
You would be surprised how many of my students just have the wrong fingerings. So look them up if the above doesn't work.
These are just SOME of the things that cause squeaks. I would need to see and hear you play in order to fully diagnose the problem properly. Any clarinet teacher can do this. You may need to have a lesson or two if you don't already. Squeaks are just a part of life