This page will provide you with some troubleshooting tips for playing the upper register. It will also assist you in playing the lower altissimo notes.
In general, issues in the upper register are due to overall technique problems.
Double check that you are fingering the notes correctly. Don't be afraid to visually confirm a note is correct.
Confirm your hand position is facilitating proper covering of all the holes. Remember to have naturally curved fingers that cover each hole with the squishy bit of your finger.
Your embouchure should be firm without biting. Your lower lip should support the reed, not dampen it. Your embouchure is not vastly different between the low and high registers.
Your air should always be fast when playing the clarinet.
Your tongue should always be in a raised position, like a hissing cat.
If all the above is correct, take your clarinet in to a qualified repair technician. A slight leak or misalignment can limit your ability to play in the upper register.
Below are audio recordings of the lower altissimo register notes and their suggested fingerings.
Basic C# Fingering
Basic D Fingering
Basic Eb Fingering
Basic E Fingering
Basic F Fingering
Basic F# Fingering
Basic G Fingering