Do not be ashamed - I imagine it's a common reaction. I know I wouldn't be particular good at handling it - lucky for me, my wife is in health care and the NHS so had no issues with all that.  Cancer is tough on the patient, the carers and family. It's okay to ask for help too :)

I would defo speak with your oncologist / cancer support team and ask for something to help with the side effects though. Something to prevent the diarrhoea should be possible and maybe dizziness.  Try and east small and often and if it's a taste / mouth issue thing for eating, ask about mouthwash or something too. First Chemo cycle is often about finding solutions to side effects.

Good luck, you got this!