Without more detail about the recipe and brewing process, we are shooting in the dark a bit.
For me, most of the plastic/medicinal tastes come from chlorophenols, which is the result of not properly handling the source water for your brew. This is true of both all grain and extract brews. The use of campden tablets or metabisulfites to remove both chlorine and chloramines from your water source should eliminate the issue. Chlorine is readily handled by filtration through an active charcoal filter, but watch the speed of filtration. Chloramines tend to break through filtration as they are much more stable, but can be consumed by active charcoal or charcoal block filters if the contact time is adequate. Campden is cheap and easy.
Another possibility is yeast health. Dramatic underpitching of yeast, stressors such as not tempering the yeast to the wort fermentation temperature, lack of temperature controls (fermenting too hot), lack of oxygen, can all promote phenolic off flavors. I have gotten big phenols from yeast that I stored improperly, despite making a starter. I suspect contamination in that batch of yeast.
Bottled water should not have chlorine, and it seems unlikely that the residual water from sterilization would cause a strong plastic off flavor. Did you use anything specifically that would add a strong plastic flavor?