Why are you running Amsoil in a Civic? You still have to change the filter frequently when you're using amsoil and add oil if needed. I know that amsoil runs forever in many cars without servicing, but I really wouldn't do it to an import. Civics are very inexpensive to maintain if you follow the factory reccommended fluids, and they have a great track record for long life without needing to use expensive synthetic lubricants.

The oil light should not come back on after you start your car. It's a pressure-switch activated light. If you're not getting oil pressure at the sending unit, your engine isn't being lubricated when that light is on. That's VERY bad. I'd do as raiden571 says if I were you. If your oil and filter are that clogged up, I'd get it all out of there and start over with what the engine's supposed to use.

If the light comes back on with fresh clean oil in it, then you have much bigger problems to worry about. Your oil pump could be on its way out. The oil pump is driven off the crankshaft. You'd need to basically do a timing belt job and then some just to get to the oil pump, and most shops are going to quote you 8 hours of labor. You have to pull the front case and replace/rebuild it, if it's worn out. Hopefully clean 30w motor oil will fix it. Good luck.