Loose steering gets looser after rough road

[Green K20]

When I bought my truck I knew it had loose steering. It wasn't enough to be dangerous. I could keep it in the lane when out on the highway.
I took it to our mechanic, who owns two 67-72 C/K pickups, and he said his 4WD truck steers the same way. I was ok with that. I drove it like that for a week until I got the idea to go muddin' with a friend of mine. We went down this minimum maintenance road that was full of big holes and ruts. It had just rained, so there were lots of big puddles.
Anyway, I found out that my truck is not ment for that kind of thing. It is too slow. I bounced and splashed my way through the puddles and ruts, spraying muddy water everywhere. Afterwards, I noticed that it wanders even more now. The already loose steering has gotten worse. Could it be the steering gearbox? What is excessively worn or broken, and how would I go about repairing it? Thank you in advance.