You say your chimney was swept and capped. It may be that sweeping only ever removes that which can be budged by the brushes and there will always be accumulations left behind in nooks and crannies.
So one possibility is, as said above, heat from next door is driving volatile molecules from the soot, to the point that you can smell them.
The law of diminishing returns predicts that you can get the chimney swept again but the contractor will struggle to reach the pockets of dust missed the previous time. So potential for expense with no improvement to the problem.
A less attractive possibility is that the chimney brickwork is cracked, internally and next door's combustion gases could be leaking into your chimney. The smell would then be the least of your worries.
Carbon monoxide is heavier than air so will work its way to your downstairs fireplace vent. However, you'll need to know if/when the neighbours are running their fireplace before you can make any sense of detector readings.
Regrettably, I cannot beginto imagine what remedial work is possible, inside a chimney stack. Does builder still post on AB?