Pressure Tank

There is water in the well. The pump is pumping water (we shut off the pressure tank and water line to the house and turned on the valve near the pump and pump and water came forth). But pressure tank doesnt seem to be filling. The pump must work very long to build pressure in the tank — it doesnt seem as fast as it used to be. So I think there is a problem with the pressure tank. It is old (15 years) and we could use a larger one (it is about 10 gallons for a 2-person household). But how can we confirm that the tank is the problem? And how do we know what size to buy? Does it depend on the output of our well? Why isnt the pressure tank filling? Our well does spew forth gravel — my washing machine water line tends to clog with it — is it possible that gravel was clogged something in the pressure tank? I did check the pressue in the tank — it was 23 pounds when empty, which is also our cut-in pressure on the well. Our cut-out pressure is 40 pounds.