Orajel is a topical pain reliever. It's main ingredient is a Benzocaine, a topical anesthestetic. It's main use is to relieve tooth pain be it caused by teething on new born, by extraction
, or by coldsores. Thus, it can be applied to open wound. This means that it should not cause any trouble for your cut. When wrongly applied, the best course of action is to wash it with a lot of water. Minimum amounts will be absorbed, so if you only applied a small amount, absorption should not be a concern. Most common adverse reaction caused by orajel is irritation and or redness of the skin due to reaction of the skin to the components of the product. If you notice any changes in the skin you should contact your dermatologist
. Alcohol swabs can make the area worse and actually cause irritation of the cut, thus it is recommended to avoid it applying directly to open wounds. Water and a little bit of soap should do the trick and then apply your neosporin as you normally would. Observe the area for any changes as mentioned, such as redness, swelling, pain, or any other signs of inflammation. This unlikely will be caused by the product, but if they are present, it may be signs that your wound is not healing well and will may need to see your health care provider.