Can trigger finger in one finger lead to minor swelling in another at the base which might lead to devloping another trigger finger?

Possibly: Presenting with multiple trigger fingers is not uncommon. Sometimes the same problem develops in adjacent fingers simultaneously. It is not likely that one finger causes the other finger to trigger, but simply that a similar process is developing.

I dont think that : Swelling in one leads to the triggering in the other. The adjacent finger may show signs of altered mechanics induced bythe triggering finger preventing full motion, especially the ring finger and its adjacnet middle and small. The adjacent finger may jsut happen to also have a trigger finger that was clincailly quiescent and it develops a bit later. But doubt it spreads by swelling, directly.