2000 Vauxhall Corsa cannot start car without reving first

Hi, my car is driving me mad!! I'm hoping somebody can help...

Since I brought the car the engine management light used to come on, stay on for around 3 minutes, in which time I'd loose power as it wouldn;t allow me to accelarate (nightmare on the motorway!) and also when I first pull off in first the car would just roll for a few seconds, than sort of kick in n shoot off. I took it to Vauxhall, they basically said they had no idea what was wrong with it but I could leave iot with them for £90 an hour! Which I decided against

I carried on driving it, but on Friday I was driving to work and the engine management light came on again, except this time it didn't go off and than the car started to jerk and wouldn't let me go over 30MPH.

I took it to a local dealer who cleaned the carbarator, the car drives beautiful now, no jerking, no engine managemnet light and no holding back.

However, the car won't start unless I rev the engine for about a minute, which I'm sure can't be healthy for the car...I've been told that it may be the 'cold start sensor' but I'm worried about wasting money if it isn't...hope somebody can help