Always avoid pouring oil and food fats down the sink. Pour them into an empty container instead and throw it away in the rubbish. Putting items like this into your kitchen drain is a recipe for disaster. Once these items cool they solidify, creating a very solid, and hard to remove barrier in your drain. Even jelly is a no-no! Just think about the globules of fat sticking to the insides of your sink pipes. Then consider the food scraps that swirl away after washing up. Food scraps will get trapped and create a worse (and smelly!) blockage.
These blockages can sometimes be removed with store bought drain cleaners, or if you’re handy enough, by removing the drainage under the sink and clearing it out. But to be safe, and to know the problem has been rectified properly, you should get a professional plumber in to review and repair the problem thoroughly.