First, is the through-hull for the water intake line clear?
Barnacles could have clogged it, as could have eel grass. If either is the case, you won't have much luck flushing.
Also, when was the last time you flushed the head vent line. You really should do this on a regular basis, to prevent it from clogging. If you've over-filled the holding tank, it is very, very likely that the head vent line is clogged. When was the last time you pumped out the tank, and was it filled to the top at the time???
Also, when was the last time you re-built the pump on your head unit?
If you can't answer that, it's probably been too long.
It would probably help if you said what make/model head you had. Some are notorious for having pump issues, like the Jabsco units.
I'd point out that pumping water into the head bowl from the sea is mostly unrelated to being able to pump water out of the bowl. The problems with one should not generally affect the other, unless the seals in the pump are completely shot.
Some heads, like the inexpensive Jabsco units, are generally not worth re-building. Others, like the Raritan PHC or PHII units are very reliable and quite worthy of being re-built. If you have a unit like the Jabsco or even a slightly more reliable unit, like the WC Headmate 90 which has been discontinued, it might be worthwhile to upgrade your head instead of rebuilding it.
Raritan offers a PHC LBA or PHII LBA unit, which is basically the entire head minus the bowl and seat. You basically take one of these and swap the bowl and seat onto it, and voila, you have effectively a brand new Raritan PHC/PHII head for a lot less money, since the bowl is one of the heavier and more expensive elements in a new head. Think of it as recycling. SBO has the LBA units for sale.
BTW, I'd point out that Peggie Hall considers the Raritan PHC/PHII to be one of the best low-priced manual heads for boats. She's basically the doyenne of the marine sanitation industry...