Hi and welcome to MM linfit
Most HRTs will start to reduce flushes and night sweats within a couple of weeks. When it comes to anxiety, it may take more time and HRT alone may not be enough. Practising some CBT and Mindful Meditation is helpful and often looking at lifestyle e.g. diet and exercise regime etc. should also be considered - there is rarely one magic fix for anxiety. Did your anxiety start for the first time when menopause hit? Have you had episodes of anxiety in the past?
I believe that once the flushes are under control and you start to sleep better, then the improvement in wellbeing will lift the mood. HRT in continuous form, as you are using, which includes progesterone all the time, can throw up issues in terms of mood and this is why we often suggest a sequential HRT to begin with, however you are starting on a good option so do persevere.
You do need to give any HRT about 3 months to really do it's magic and perhaps try something different if this one doesn't work. Keep us posted. DG x