Hi Audrey,
Kris too does all his swallowing standing up, then it's just tip and swallow. Being in a good upright position certainly does help to avoid any reflux. I would be asking your team for some antiemetics - that's anti nausea medication. I would suggest taking these regularly. Some of these meds help with gastric peristalsis - moving stomach contents on down through the bowel so they don't pool in the stomach and can't be regurgitated.
I would also ask for a proton pump inhibitor such as omeprazole which would improve any reflux that may be causing a problem.
Hope this helps, Tammy.