Here is a link to the Shop Manual for the oil pump removal and service. This is for the 1955 2nd truck, but I believe that the oil pump on yours is similar. If you decide to remove the pump, do not attempt to remove the two large rivets that attach the oil pump mounting fitting to the block. Just remove the large set screw.

If there is too much oil in the pan there could be a problem as the oil could be thrashed around by the crankshaft and become aereated and not pump very well. I would remove or drain any excess oil; better yet, drain it all and add the correct amount of fresh oil.

It is hard to believe that the pump would suddenly go bad, but it is possible.

Good luck.

Hoyt