A tickling sensation in your lower teeth and front gums could be caused by a number of things. Part of the solution and the cause depends upon your age. If a child has the sensation it could mean they are about to lose a tooth. If you are an adult it could mean that you are about to get sick.
Many children and adults who have allergy problems experience these symptoms on a regular basis. In most people this is a sign that you have recently had a cold or allergy bout or you are about to get one within the next week or so. Having the coughs for a period of time can also trigger these symptoms. The feeling may even move into your lower jaw. If you are having a cold you'll experience these symptoms most often when you exhale, and the feelings can last for an extended period of time.
There is really nothing you can do about this situation other than wait it out. What a person is feeling in most cases here is the nerves in your teeth and gums reacting to something. Don't worry about it and try to ignore it and in most cases the sensation will be gone before you know it. In rare cases it can be a symptom of tooth problems, most likely a problem with a nerve, but in those cases the feeling will not subside and is accompanied by tenderness and pain in that area of the mouth.
In most all cases, having a tickling sensation in your bottom teeth and lower gums is nothing to worry about. It's just a sign that your nerves are alive and kicking. Try your best to ignore it and go about your business and it will be gone before you know it.