I tend to be a science/math and logic driven person… My problem is that I believe everything with my brain, but it’s harder for my heart to catch up.
It is good that you recognize the necessity of faith in your heart. You mentioned two different emotional aspects: feeling the Holy Spirit, and being emotionally pulled to the Church. I would suggest looking at it yet another way: Relationship. More specifically, personal relationship. Even more specifically, personal relationship with Jesus Christ.
I am a bit like you. I love the Catechism and the Bible, making logical connections, and finding answers to questions. In the last couple of years, I started reading other kinds of religious books. I noticed that many saints have a real one-on-one relationship, like a friendship, with Jesus.
I read and thought about what the Incarnation means – God became human, a fully human person, not just 2000 years ago, but eternally, and right now. Fully human and fully divine; earth and heaven are joined. God is near us. Jesus Christ is present in the Eucharist, of course, but he is also right there when we go to Confession and in all the sacraments.
I realized that I had been overlooking that personal connection, and I resolved to make my faith more personal. I am still working on it. It doesn’t exactly come easily to me, but I am praying more often, mostly small prayers, asking for help, giving thanks, and simple praise. I try to be more aware of the active presence of Jesus in my everyday life and in the world.
You used the word heart, and that is excellent. You want your heart to be involved/engaged in your faith, and you want your heart to be filled with love, joy, and peace. Bring your heart to Jesus and I believe it will happen.