I’m wondering if the Church frowns on the genre in which I write as a hobby. Is there any specific prohibition on this style of writing?
No, there is no Church prohibition against writing romance novels, particularly since you are apparently writing them for your own pleasure and not necessarily for publication. But, should you be working toward publication, given current standards in the genre that predominantly demand “sexy” romances, you may wish to take an interest in informing yourself of the Church’s teaching on morality, particularly the virtues of modesty and chastity, and sexuality, perhaps with an emphasis on John Paul II’s Theology of the Body. As a Catholic author, the privilege of publication should call you to the responsibility of writing romances that both uplift the human spirit and uphold the value of traditional marriage. You may find the references linked below to be helpful.
Deus Caritas Est by Benedict XVI
Love and Responsibility by Karol Wojtyla (John Paul II)
Theology of the Body by John Paul II
Theology of the Body Explained by Christopher West
How to Read a Dirty Book by Irving and Cornelia Sussman