Thank you for the query.
From your description what you have in the cut area is scar tissue creation (it would be much easier to answer your question if you attach a photo of it). During this process, immune system cells (leukocytes
, macrophages) migrate to the area. This needs blood vessels widen and blood flow though this area rises. This causes mild swelling, redness
However if the pain and significant swelling appears with wound discharge, an infection might be present.
If there is no infection, after few days from a cut, no need to clean in with some special agents. Water with soap (sound simple but is really a good solution) is enough. No creams are necessary. You may use some scar agent if you want the scar to be less visible (like Mederma Scar Gel).
Hope this will help. Feel free to ask further questions.