I do think that it is difficult without further information. This is what I think is relevant:
I am presuming they had access to information from your previous appointments
Has this medication been tried before, and if so did you tell them?
Depending on the situation, a month could be a reasonable trial of this medication - do you have any reason to think it shouldn't be tried?
Have you been given follow-up information - such as 'come back in a month's time to discuss how the trial has worked' or 'if you see no improvement by [a certain time] please make an appointment'.
These flow charts / algorithms are very useful. They are a way of ensuring that things are not missed, and as a nurse practitioner I used them a lot.
I would consider why you don't feel you have been heard properly by the doctor. Is it because you have a feeling that this medication isn't the right thing for you? Think about why.
Is it because these are worrying times in the NHS and we are all a bit on edge?
Did you not feel comfortable with this doctor - because they are a 'trainee' or some other reason?
8 months is quite a long time - is your problem worsening or not going away? Or i it one of those intermittent issues?
In this situation you do have a right to discuss with someone else, you also (IMHO) have the responsibility to consider the use of NHS resources. If you do ask to see someone else, I would try to pinpoint what you feel the problem is. Sometimes when we are upset and anxious that is difficult
I do hope this is helpful and that you can resolve it.