Welcome to HCM.
Do not worry, since you do not have a history of any oral abnormalities, then it is probably just a line of oedematous tissue, developed due to chronic physiological irritation of the Buccal Mucosa rubbing on the line of occlusal contact of the maxillary and mandibular teeth, called the "Linea Alba", which is completely physiological, and no treatement is required for the same.
However, if you have a chronic habit of biting on your cheek, then it is a lesion called "Morsicatio Buccarum", (commonly known as "Chronic Cheek Biting"), which has, though very rarely, still been sometimes reported to be a pre-malignant lesion also, so you need to be careful.
Consult a good dentist
, who will tell yo the proper treatement.
Surgical excision of the white tissue tag may be a good option, but incase there is less space between your cheeks and teeth, then there is still going to be more irritation of the wound by the teeth, which will delay healing and can still cause an oral Squamous Cell Carcinoma
, so, not going for any surgical treatement, and just using a proper Oral screen would be a better idea.
Also, incase you are over-weight with puffy cheeks, then shedding-off the extra pounds will also help, as when the "Buccal pad of fat" lessens, it will then increase the area between your teeth and buccal mucosa (cheek mucosa), eliminating the impingement of your buccal mucosa on to your teeth.
Wish you all the best.