I have recently had the hicups following my sixth cycle of chemo. The oncology nurse mentioned that anti-emetics (anti nausea medications) frequently take care of the problem. You may want to ask.
A flight attendant I knew said the best cure was to tightly wrap a paper towel over the top of a large, full glass of water and drink through it. It works because it forces you to drink slowly, or take little sips slowly.