Been a while since I played CIV3. Are you playing the original version or Conquests?
The furthest that I reached was Emperor level which I could usually beat but not guaranteed. As you move up in levels, winning on a Pangea map becomes increasingly difficult. At Emperor level, continents maps are playable but tough. What I would say is that if you are building hospitals, your strategy is probably not optimal. At Emperor level you need to build as many cities as possible. Your core cities shouldn’t have the space to reach size 12 let alone expand beyond it. You need as many cities producing military units as possible. At Emperor level, you can usually forget about cultural or spaceship victory. You need to survive to the industrial age, railroad every hex in sight and prepare for war. Build lots of artillery units, bombers and and prepare to bombard enemy cities into submission. Be prepared to put craters in every enemy tile. The AI is incapable of doing this and the fact that it is fundamentally dumb will give you the chance to overcome its production advantage. You cannot hope to keep up with the AI in scientific research: as already suggested, you need to look for opportunities to trade tech. Keep a constant eye on the techs held by your opponents and look for the opportunity to exploit a gap in the market. If you see another CIV acquire a tech that others lack, try to trade for it straight away and sell it on. If you don’t, the tech will be traded by the next game turn to every CIV with which the first CIV has contact. As a general rule, you need to be opportunistic. Don’t start a war with another CIV unless this already fighting for its life or has been weakened by an earlier conflict.
Also, I wouldn’t choose the Americans if I wantEd to maximise my chances of victory. Their specialist expansionist trait is virtually useless on an archipelago map and if you haven’t already won the game by the time their special unit comes into play, chances are that you are not going to. Moreover, it is virtually impossible to get a golden age when the special unit arrives so late in the day.
https://www.civfanatics.com/civ3/strategy/introductory/civilizations-from-easiest-to-hardest/