you coulod possibly be a diabetic
i agree with @CStatic... try a disinfectant or a n antibiotic to prevent the cut from worsening, and use something like polysporin to help with the irritation of the skin. hope this helps!! best of luck :)
Only reason I can think that it would bleed for so long is that it was deep, or you are low on Vit K and or iron. As for tingling, burning, pain that makes me think either you cut a nerve (that would be deep I would think) or have an infection. Swelling, and rash also make me think infection. One other off the wall possibility, if you had the beginning of a herpes blister and nicked it, then it would bleed for a long time as herpes blisters once open ulcerate and take forever to "scab" up as well as travel along the nerve causing pain before erupting into another patch of blisters.. if no blisters watch for other signs of infection like red hot skin, swelling and pus.