I have noticed that while trying the advanced lip trill my throught will become a bit itchy when trying to get to the higher notes. Should I stop when the itchiness starts and wait or stop, wait and move on with other vocal exercise?

Hi, Ninoshka! 

Itching in your throat is a sign I'd pay attention to. See if you can modify the exercise in such a way that the itching goes away: less breath pressure/volume, or changing to another SOVT like singing on an MM, NN, NG, tongue trill, VV, BB, or ZZ. You've got options! 

The lip trill often causes a harmless itching in your nose or upper lip from the vibration, but I haven't experienced itching in the throat, and that's not something I'd recommend you push through. Try the above configurations and let me know if they work instead!