What if my counsellor tells me that we have to talk about issues that I find uncomfortable

No counsellor should make you talk about anything that you do not want to talk about. It is unprofessional to make these demands of a client. In fact, the counsellor would find it impossible to force you to discuss things with which you are not comfortable. In this respect, the power to make the necessary decisions lies with you.
However, sometimes a talking treatment will be effective only if you are willing to look at areas of your life that are complicated, painful or which you would rather leave alone. This does not mean that you have to go ahead against your will, but it does mean that you will have to accept the consequences of not discussing whatever the subjects are that you want to avoid. Occasionally this is a major block to progress.
For example, someone with a drink problem will not make many positive changes if he or she is unwilling to discuss alcohol. The possibility that you are missing an opportunity has to be acknowledged whenever you decide to impose these kinds of “no-go areas” on sessions. Sometimes we avoid subjects out of loyalty. Perhaps we do not want to talk about our family because we think that it is wrong to criticise the people we love. On other occasions a trauma may be too distressing to discuss in detail, or even to mention. There are many reasons why it can be easier to stay silent. You may nevertheless find it helpful to discuss the reasons why something is difficult, and you can do this without necessarily discussing the issue itself. A discussion may reassure you that the counsellor is sympathetic and will not judge you. It may be useful just for both of you to know that there are areas that have to be left untouched, because this could be an important “boundary” to agree upon. This may also leave the door open to returning to these subjects later in the therapy, when talking about them may feel less threatening or less uncomfortable.
The counsellor should never try to drag words out of you, and there is no pressure on you to walk into your first session and immediately tell me the story of your life. It may take time to get round to all the things that you want to talk about. Try to keep an open mind on what you may eventually want to discuss, but remember that you are the one in charge.