Hello & welcome,
Bleeding from the wisdom tooth after brushing especially when the wisdom tooth is partially erupted in the oral cavity is very common & is absolutely normal.
It may happen due to accumulation of food debris or plaque
layer over the partially erupted wisdom tooth leading to inflammation of the surrounding tissue making it prone to bleeding even on slight touch.
Whatever you are seeing hard stuff in front of your wisdom tooth, i would advise you do not try to take it out on your own as this may lead to infection if you hurt yourself. Even there are chances of bleeding.
Visit your dentist
& get your oral cavity examined clinically. Ask your dentist to remove the thing which you are seeing in front of the wisdom tooth.
Keep your oral cavity properly cleaned to avoid gingival inflammation