Ok, thank you. In a younger cat like this my first concern is always a foreign body that is causing an obstruction in the GI tract--even in cats that are well monitored, they can eat something they shouldn't and it can get caught anywhere along the way from the stomach to the colon and cause a problem. We will generally see a decrease or absence of appetite, a lot of vomiting, meowing which can indicate pain and lethargy as they get weaker from dehydration.
However, vomiting and decreased appetite can be caused from several things: kidney
and liver conditions, urinary obstructions, toxins, intestinal parasites are all possible causes. Because it has been a week, I have to advise that you get him seen--at this point he is very likely getting dehydrated from the vomiting, so at the very least he most likely needs some fluids.
Unfortunately, there is very little that you can do at home in a case like this. If he can't keep anything down, there is nothing that we can give over-the-counter to help as he will just vomit the medication right back up. If he's not eating, trying to feed a bland diet is not going to work.
I hope this information is helpful--if I can help with any other questions, or explain anything further, please just let me know!