A small amount won't hurt you, it'll be very uncomfortable. The danger from these products near the groin and especially the anus is they contain a chemical (Methyl salicylate) similar to aspirin (acetylsalicylic acid) and those areas will readily absorb the salicylate through the skin. Too much can cause the same liver issues as overdosing on aspirin.

You didn't apply nearly enough to be worried, but probably avoid taking any aspirin for the next day just to be safe.