no you will not get tss from a piece of condom (most likely latex not rubber). if there is a retained piece it will not likely cause any problems but you can carefully check with your finger or use a gentle warm water douche to wash out any possible remnants.
my boyfriend and i had sex using both the pill and a condom. the condom broke. should i worry about rubber inside me? . we think most stayed on his shaft and i found a small piece about 3/4 inch x 1/2 inch. like it ripped and a portion tore off. do i have to worry about this causing tss? .