Chemotherapy causes hair loss by damaging the fast-growing cells that line the hair follicles. The bumps you describe could be caused by irritation or inflammation, which many cancer patients experience after hair loss. Or it could be that oil from the pores is clogging the hair follicle, causing a type of whitehead.
How sensitive is your scalp? This could be a clue to what's going on. Consult your doctor and have her look at your scalp. If the bumps are oil-clogged pores, exfoliating gently would help release the oil and clean out pores. But if the problem is irritation or inflammation, then exfoliation would not be a good idea.