Hello I am Dr. Joey. Thanks for trusting me to help you and your pet today. I am a licensed veterinarian with over 16 years of experience. I look forward to working with you.
Based on what you have written I am quite concerned about Romeo. It is always okay to give vomit/diarrhea a day or so but then if it was just something passing it would be resolved. For it to persist for more than 48 hours puts him at risk for severe dehydration and also suggests there is something significant going on that is probably not going to resolve on its own. Therefore, the absolute best plan for Romeo is to have him seen by his veterinarian as soon as possible today. He needs an examination and then some testing which might include lab work (CBC, chemistry profile, urine check) +/- X-rays to try to narrow down the problem.
Unfortunately his symptoms are vague and I could not provide you with an exact diagnosis for the cause. It could be anything from ingestion of an unusual item (or toxin) which has upset his system or is trapped within his system to organ failure (liver, kidney) to pancreatitis to infection (bacterial, viral, fungal) and the list continues.
If it had not been going on this long I would suggest some at-home things you could try but at this point now that he is shivering and lethargic I worry he is critically dehydrated and may be febrile which are not things you can contend with easily (and safely) at home. I also fear anything we try to do at home will not work because they must go by mouth and he is vomiting. Therefore, nothing will stay down long enough to work.
I regret I am not providing good news or an easy at home solution for you. I am also at a point I need to know what questions you have. If I have misinterpreted and he is not in this serious a condition as it sounds or this has only been going on 24 hours, then let me know.
I hope that the information I provided has been helpful.
Please let me know if for any reason you need further clarification, have more questions, or were expecting a different type of answer. If you received all the information you needed, then kindly submit a rating.