Just because it's in a plastic box doesn't mean it's not shielded.
However, just because the inside is coated with something conductive, or the case is made entirely of something conductive, does
not mean that the screening is effective. Lots of these commonly available polymer enclosures with internal conductive coatings offer very little screening effectiveness over those that are uncoated. The reason for this is in the fine detail - no provision for conductive gaskets, the bending moments between clamping and/or mounting screws, lack of conductive conversion coatings, moulding flash, inclusions... The traditional "London" style rig (the folded box) is about as ineffective as they come - but it's not really relevant, as you're interested in generating high field strengths anyway.
Besides, interference at around 100 MHz will be coming from the input and/or output leads, not from directly inside the case. It may have been generated inside the case, but it won't directly radiate from there very well. Stick a ferrite or two on the leads and see if that improves it.
If something of yours is interfering with your radio, take apart and find out whether it's screened, and whether the input and output leads are filtered (at all). You might be glad you did, as you might find some horrors in there and may never want to turn it on again for fear of burning your house down.