Having had the same experience myself, I want to re-empathasize what Brian stated: Constipation can cause ALL of those issues. For many of us here it was the WORST part of treatment - worse than mouth sores even. I spent many days, curled up in a fetal position, on the bathroom floor. Constipation causes stoppage of homeostatis so, yes, everything in the stomach will be evacuated orally. Narcotics can cause this VERY rapidly.

Get to the hospital nutritionist right away.

As David posted STAY HYDRATED, this will help with the constipation and the fluids must be replaced if he is vomiting.

All the posters here have offered good suggestions, feeding techniques, etc. So you will have to experiment with different methods to see what works. Be patient it's not easy (what an understatement).

No one mentioned antacids, but Cisplatin does a number on the GI tract so talk to the MO about that as well.

This situation could get out of control very quickly.

Kudos to you for being a great and loving caregiver - it is much harder than being a patient. I have done both so I speak from experience.