Put the original carb/jet back on and exhaust if it's not rusted out beyond use since those are the only two performance mods you've done to it. You can't tune it or do upgrades until you get it to run correctly.
If you take the carb and pipe out of the mix and it runs right, then you know the issue is from one or both of those parts.
If you take it back to all stock and it sill does not run right, then its an issue with something else you messed with.
Here's my restored Si: