It really depends upon the drainage you have added to the compost in which you sowed them. If you added things like fine grit, vermiculite or similar, they should be OK, as long as the container also has good drainage holes. Lifting it up is a good idea. Covering carrots with horticultural fleece is always a good idea, as it keeps the dreaded carrot fly away - they can't find the carrots then. If the seeds have got pushed too deeply into the soil by the rain, they may not be able to germinate - but there is plenty of time to resow if this does happen.