I hate to say it, but it sounds like you have may either have a bad catalytic converter or a dead cylinder.
A bad or plugged up catalytic converter can contribute to bad acceleration and increased fuel consumption. However, vibration/shaking while at idle is usually caused by an engine misfire.
With a misfire, one or more cylinders are not igniting the fuel-air mixture in the cylinder due to either bad compression, no/weak spark, no/wrong mixture of fuel. Since the cylinder doesn't fire, the gas isn't burned all the way or at all and it just goes out the tailpipe. This ruins the catalytic converter in the process.
The reason why I'm leaning more towards the weak cylinder is because you have a 98 Tahoe, it is ODBII and the check engine light comes on when a cylinder misfires. However, there are many things that can contribute to a cylinder misfire. You said you changed your fuel filter, and spark plugs. You may want to change your Distributor Cap and Rotor and your Spark Plug Wires.
After this, if you still get the vibration/shaking at idle, you need to do a compression test. You can bring it to any shop to have this done, or you can buy a kit yourself. Since your truck is ODBII it would be quicker/easier to go to a shop because they can look up the code to see exactly what cylinder(s) is misfiring.
It may be something as major as warped cylinder heads or bad piston rings/seals, or something as "minor" as a blown head gasket.
I have a 95 Suburban and I lost compression in my #7 cylinder. It turned out to be a blown head gasket. Once I had the problem fixed, I still had to get a new Catalytic Converter because the misfiring cylinder ruined the old one.
Good luck, I hope I'm totally wrong, and it's something minor. A dead cylinder is no fun. And fixing it can be very expensive.