Yield stress fluids, such as toothpaste and mayonnaise, consist of soft particles suspended in a Newtonian solvent and are jammed beyond the random close-packing fraction. These materials show characteristics of weak elastic solids when applied stress is below a threshold known as dynamic yield stress, and they fluidize according to power-law fluid behavior above this limit. The rheological behavior of these suspensions is influenced by the introduction of attractive interparticle forces that arise from van der Waals forces, depletion interactions and in some cases from physical particle interactions where short alkane chains on particles form bridges with other particles to form adhesive contacts. In this regard, we study the rheology of yield stress fluids with attractive interparticle interactions, which are critical in applications such as food, cosmetics, coatings, and pharmaceuticals where precise control of flow behavior is essential, and control of stickiness gives a knob to control the rheology. The presence of interparticle attractions introduces complex rheological phenomena, including formation of clusters and shear banding. We present a computational model that incorporates Hertzian contact mechanics for nonlinear repulsive interactions and introduces a short-range "sticky force" to capture interparticle attractions. We explore the interplay between the strength of flow and attractive forces and their effect on the rheology of these suspensions. Our rheological data from the model shows that the strength of flow becomes more dominant as shear rate increases, whereas attractive forces prevail at low shear rates, highlighting a rate-dependent transition in the governing stress mechanisms. We show that increased attraction strength leads to higher dynamic yield stress due to enhanced resistance to flow. The microstructure of these suspensions reveals notable anisotropy in interparticle contacts driven by attractive interactions, with the formation of distinct accumulation and depletion regions. The two-dimensional pair distribution function shows the introduction of a second band with accumulation and depletion flipping between the bands, while the three-dimensional pair distribution function shows a transition from a single peak to a dual peak as attraction is introduced and intensifies with increasing attraction. The mechanical response of these suspensions shows stronger attractive forces maintain particle clusters however, there is a breakdown of these clusters as shear rates increase. We present a universal flow curve for sticky yield stress fluids by rescaling flow curve data with yield stress and relaxation time to collapse across varying attraction degrees. The model's predictions are validated against experimental and simulation data, providing a robust framework for understanding and controlling the rheology of sticky yield stress fluids.