yes. 3/32" is smaller than 1/8" Chains are meant to be used with certain size cogs (i.e. 3/32" chain works with 3/32" cog. 3/32" refers to the width of the cog's teeth). you can use a 1/8" chain on a 3/32" cog if necessary, but not the other way around.

you may want to take it to your local bike shop or have a friend who knows a little bit more about bikes take a look at it. this sounds like a peculiar problem.