Skin swelling can be caused by many different things. Simple problems like bee stings or mild allergic reactions can be treated with first aid. However if the swelling is due to a more serious underlying problem (e.g., a traumatic injury or edema)then you will need to seek a vet immediately. Edema is a type of swelling that is caused by fluid accumulating within a tissue. A good way to identify edema is if you push on the swelling and it leaves a dent in the skin.