i have the same thing, tricia.
it may be celery leaf miner (or any other varient leaf miner) - the flies lay eggs into the leaf (you can spot little dots, like someone has stabbed the leaf repeatedly with a very fine needle), the larvae eat the inside of the leaf, making it blister and brown, then emerge and the cycle begins again. 21 day cycle
i have only just found out myself - i too thought it was lack of watering, or something. have now picked all the affected leaves off and will keep doing that until the pest is under control. :)
burn or dispose of the leaves, not the compost heap.
other plants that may be affected: celery, lovage, parsley (yes i found some there :() and also my parsnips.
hth
svea