From the details you have provided, it is evident that your constipation has set off a reaction which began with itching around the anus followed by pain and bleeding while straining during defecation. The possibilities are either haemorrhoids or anal fissure and it needs to be clarified and I suggest that you consult an ano-rectal surgeon (or a gastrointestinal / general surgeon) for a correct diagnosis as the treatment differs with the conditions. I suggest you use mild laxatives to keep the stools soft and use local anti-haemorrhoidal gel / cream till you consult an appropriate specialist.