I am a singing teacher. The reason for getting you to singer higher than you are accustomed to is to open the voice up to extend the range - improve the tuning and add resonance to the voice. Remember also you have only been singing a few months. The full effect of the lessons will only take effect over a period of time. I would raise the issue with the teacher concerned. As the higher range gets more resonant you will see more quality coming out in the sound. But your voice is a work in progress and will sound better as you develop more support on the higher notes.

I have added 3 - 5 notes on to some singers voices and raised their whole range by 2 - 3 notes giving them a more effective sound. This does not mean that they use the higher register all the time but is there when needed and also your voice will sound more relaxed and resonant in its middle range

I would also suggest singing a song in several keys - one for singing lessons and one for performing and work out over a period of time which is best.