Some people might recommend that you visit another parish on a Saturday afternoon, where you can confess to a priest you don't know. Others might suggest that you confess behind a screen to any priest, for privacy. While you're free to do either of those, I don't think that really gets to the heart of the matter. You just feel uncomfortable with confession. And you know what? Don't worry. You're normal.
Jesus knew that going to confession would not come naturally for us. We'd much rather ask his forgiveness while sitting in the privacy of our own rooms. But he instituted the sacrament of reconciliation anyway (John 20:21-23). Why would he do it? For the same reason a father allows his child to be given a shot of medicine. He knows the kid would rather not receive an injection, but he knows how it could be life-saving. The kid simply has to trust that the Father knows what's best.
Now, I don't really like the analogy of getting a shot, because kids don't look too thrilled afterwards. But have you've ever watched people's faces as they go to confession? You'll notice as they enter they often appear apprehensive and weighed down. But when they leave . . . I'll just let you see for yourself the difference.
It's often forgotten that confession does not just take away your sins. It gives you powerful graces to avoid those sins in the future. It also helps you to listen to the Holy Spirit better, and it gives you peace of soul. But if we want all of these graces and gifts, we must humble ourselves. I was once in a church in Europe where they built the doors three feet tall. It looked like munchkin-land. Anyone who wanted to enter had to bow down to get in. Otherwise, they would just be left outside and would not get to see the breathtaking view inside. It's the same with confession.
As embarrassed as we might be about our sins, St. John Vianney reminded us that, "Our sins are nothing but a grain of sand alongside the great mountain of the mercy of God." Now, although I know your sins don't feel like a grain of sand, and you are concerned about what the priest will think of you afterwards, consider this: One high school chaplain I know said that when students come to him and openly confess serious sins, they inspire him. This is because he notices that the teens care more about what God thinks of them than what he thinks of them, and this takes a lot of humility and courage. This priest also said that after confession all he sees a person as is the clean soul that walks out the door. Therefore, I recommend you find the holiest priest you can, and consistently go to him for confession. This is hard, because it is all the more humbling to have to admit to falling in the same area perhaps time and time again. But this is not only great for increasing in us the virtue of humility, it helps him to give us much better spiritual direction. If we hide our wound from the physician, it will be slow to heal, and is likely to get worse.
Often we're embarrassed to confess to a priest we know. Is it because the priest will see us a lot? Is it because the priest is a friend? Is it because he is a holy man? If so, then why aren't we embarrassed to confess to God in privacy? He sees us nonstop. He should be our best friend, and is Holiness Himself! The source of our embarrassment is not our sins. It is our pride.
Lastly, consider the advice of St. Faustina, who recommends three things to the person preparing for confession: The first is that the person practice complete sincerity and openness. She says, "An insincere, secretive soul risks great dangers in the spiritual life, and even the Lord Jesus Himself does not give himself to such a soul on a higher level." Secondly, she recommends humility: "A soul does not benefit from the sacrament of confession if it is not humble. Pride keeps it in darkness. The soul neither knows how, nor is it willing, to probe with precision the depths of its own misery. It puts on a mask and avoids everything that might bring it recovery." Finally, she speaks of obedience: "A disobedient soul will win no victory, even if the Lord Jesus himself, in person, were to hear its confession."
So, when we run from confession, we are running from mercy. Or, in the words of St. Augustine, "In failing to confess, Lord, I would only hide you from myself, not myself from you."