Dear Bek,
I'm glad that you are co-operating with the grace of God and sincerely exploring the Catholic faith! I wish you all the best on this faith journey, and I hope to be of some assistance for you along the way.
Now, as you have mentioned the Catholic Church holds onto both Sacred Tradition and Sacred Scripture. However, these two fundamental pillars of the Church are not an either/or distinction. Unlike the relatively modern Protestant idea of 'sola scriptura' (the bible alone is all we need), the Catholic Church has always held onto both Tradition and Scripture.
When you quote a single passage from the bible to disprove the idea of Tradition and Scripture, you are working backwards. The first questions you need to ask are: What is scripture? Who decides what books are in the bible?
St. Paul says in the quote you mentioned, "All scripture, inspired by God, is profitable...". How do we know that 2 Timothy is a scripture inspired by God and is not just another letter/book?
After recently taking a course called "Bible through the Ages", I have learned how important these questions are. The Bible itself is a tradition, the books that are in our Bible today are passed down from our Catholic tradition (the Holy Spirit guided the Bishops in this process). When Paul was writing the letter to Timothy, all of the books in our current bible hadn't even been written yet! Nowhere in the Bible does it tell us which books should be in our out.
In the same way, what are we to do when we have a disagreement on the meaning of scripture? The meaning of the scripture in your question is important, and there can be many different interpretations. Since the Catholic Bishops (under the guidance of the Holy Spirit) selected which books that were to be in the Bible, there is nothing in the Bible that contradicts Catholic teaching (otherwise it wouldn't be in!). Christ gave authority to the Church (Matthew 16:18); this authority includes but is not limited to selecting the books to be in the Bible, and interpreting the Bible.
It's important to note that this is not a case of the chicken and the egg. The Bible came from the Tradition of the Church, not vice-versa.
God bless,
Mr. Mathew