Brief Answer: PLICA
Welcome to HEALTHCARE MAGIC..
I have gone through your query and can understand your concerns..
As per your complain the small skin tag under the tongue is not any pathology but it is a normal anatomical structure present in all the humans and it is known as Plica Fimbriata and it is present on both sides of midline and you need not to worry about it as it is nothing harmful..
Mostly people have small triangular horns of mucosal folds on either side of the midline on the underside of tongue while in some it can be a little bigger and prominent..
If you take a keen look at it, it will be present on the right side also..
If you still have any doubt you should consult an Oral Physician and get evaluated..
Hope this information helps..
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Thanks and regards..
Dr.Honey Nandwani Arora..