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Since this conference is very important I would advice you to consult your family physician, so that he/she can examine you and rule out any obvious causes. However based on your symptoms this is likely due to hemorrhoids which may cause painless bleeding during bowel movements. These veins veins around your anus tend to stretch under pressure and may bulge or swell, and constipation may be the causative factor.
Hemorrhoids is a common problem and almost 50% of the population will experience symptomatic hemorrhoid disease at some point in their lives. Basically the treatment for these symptoms are a high-fiber diet and adequate fluid intake. Please avoid using topical steroid cream, which should be used only for a week and only when there are symptoms such as itching, burning, or irritation. Another beneficial recommendation is soaking your anal area in plain warm water 10 to 15 minutes two to three times a day. Also please use wet toilet paper that does not contain perfume or alcohol after a bowel movement. Please go to the the toilet only long enough to evacuate the lower intestines and avoid prolonged sitting. Most hemorrhoids will resolve spontaneously without any medication or surgery, or with conservative medical therapy alone. However they may recur and the recurrence rate with nonsurgical techniques is 10-50% over a 5-year period, whereas that of surgical hemorrhoidectomy is less than 5%. So this condition is not a cause of concern, and will subside in a few weeks, but if it does not subside then surgical or in office therapy may be required for some patients who have persistent symptoms even after 1 month of conservative therapy.
Regarding amoxicillin continuation please consult your doctor about this since he/she knows your history better and will know the cause for the bleeding after examination. However if this was due to hemorrhoids I would advice against continuation.