Contacts still appear on phone after being deleted

After deleting an old contact and replacing it with a new one, the old contact still shows up when you try to text that person. It shows up under other and the old number but when you go to the contact its not there. Im not synced to anything but my icloud and it only shows the new number. I had this problem before and solved it by restoring my phone to a new phone but the problem happened again even though I have already replaced some old contacts and the problem didnt have. Is there anyway to fix this without having to always restore your phone as new phone. This problem is really annoying and I know many people are having the same problem. Please help! Thanks