We're the last of three houses which drain into the road ie, we're the one furthest away from the road. On the two occasions we've had problems there has been something not completely blocking the drain but just preventing water running away as quickly as usual (we suspected nappies on one occasion). This resulted in water collecting in the drain rather than running away immediately, so we had the bubbling and the smell. It did drain slowly, so no overflowing; if you can minimise your water usage until Wednesday you will probably be OK - quick showers, only flush solids and every third wee etc.
I've never called out "professionals", so I can't help with costs of Water Board/Dyno Rod etc.