If you are concerned about a lesion on your thumb, you should see your primary care doctor
or other healthcare professional for formal evaluation. Skin lesions near the nail can have multiple causes, some benign and others more concerning. A common cause of chronically irritated, dry and cracking skin is eczema. This is a poorly understood condition of the skin, typically instigated by dry skin, that results in local inflammation, flaking, bleeding
and pain. It can be unsightly to patients and uncomfortable. It is typically managed with lotions and petroleum moisturizers. With possible involvement of the nail, one must consider fungal infections of the nail, which can cause, brittle, flaking nails and discoloration. This typically starts at the tip of the nail and works towards the cuticle. Given the duration of the lesion per your comment stem, it is less likely that this is related to an acute infection. An additional possibility is skin cancers, though these typically grow over months and would likely result in severe skin breakdown. If you have darkened discoloration of the skin or under the nail (brown/dark discoloration) it is important to be seen by a dermatologist
to rule out melanoma. Given the duration or you problem I recommend that you see a doctor to come to a diagnosis and seek treatment, if necessary.