The Church has gone through a number of changes in how she practices the Sacrament of Confession down through the last 2000 years. It was once done publicly (seriously!). Penances at that time could last for years! As the Church has changed some of the ways she does Confession, she has never made it optional. When we look at the Scriptures we find the requirement of verbal Confession to be everywhere.
One of the most significant (and good and proper) aspects of the change of Confessional practice is that it is now allowed to be private and anonymous. This is the value of a good old fashioned screen in the confessional. Yes, there are many confessionals that have been converted into something that resembles a psychiatrist's office (as though Confession is supposed to be a "chat"--it is not), but time has shown that this is not helpful (and maybe has even driven people away from Confession).
In connection with this, it is also the case that Catholics can go to any Priest to say their confession. I have had people tell me they cannot come to me to say their confession because they know me too well and do not want to ruin our relationship (they forget that I rarely know who is behind the screen, but that is fine). Others will tell me that they have to come to me for confession because they know me so well that they need to have me be the one to help them with their struggles. Fine either way. You can come to your own parish Priest or go to another. Because the Church wants to allow you to open up in Confession so that you receive the greatest benefit.
Assuming that the Priest is performing a valid Sacrament (more on this in another post), it does not matter who you go to. I cannot say this enough: Go To Confession.