As lurkingforacure said, your dad is very lucky to have you. So many side effects from medications are brushed off aS a virus or something else. You make it sound as if he has not had such problems until he started the Sinemet.
SeVere nausea is not uncommon when starting Sinemet (generic name carbidopa/levodopa). Taking his dosage with a small carbohydratE snack might be helpful. Foods high in protein tend to weaken the potency or efficacy of the medication. For detailed info on most medications, visit www.rxlist.com
Specific info on how the mechanism works can be found here
If your dad has been taking Sinemet for several months, possibly as little as several weeks and his diarrhea and vomiting just began recently, it is probably unrelated to the Sinemet. However, do NOT stop taking Sinemet abruptly without your doctors' direct observation, as a fatal reaction can occur (neuroleptic malignant syndrome)
Best to you, and thank you for being such a good caregiver!