1994 Lincoln Continental car shakes when accelerating

Couple of things. For awhile when driving if accerate wouldn't shift past second gear and would have to shut off and restart. For example if taking a turn you slow down to about 20 mpg and if you don't let it shift down before you accelerate then it woouldn't shift past 3rd. Now when you accelerating between 20-30MPH if you have the gas down to far the car shakes. Once past 30 stops. You can' floor the car at all or take off fast if you need to get moving. Any thoughts?

Was thinking of replacing fuel filter because it probaby hasn't been done. Also was going to have the transmission look at.