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Two Dehn surgeries on a knot are called cosmetic if they yield homeomorphicthree-manifolds. We show for a certain family of null-homologous knots in anyclosed orientable three-manifold, if the knot admits cosmetic surgeries with apair of positive surgery coefficients, then the coefficients are both greaterthan $1$. In addition, for this family of knots, we show that $1/q$ Dehnsurgery for $q$ at least $2$ is not homeomorphic to the originalthree-manifold. The proofs of these results use the mapping cone formula forthe Heegaard Floer homology of Dehn surgery in terms of the knot Floer homologyof the knot; we provide a new proof of this formula for integer surgeries in$\text{Spin}^c$ structures with nontorsion first Chern class.

Heegaard Floer Surgery Formula and Cosmetic Surgeries