If you've allready put $5500 into this car that's now probably worth about half that amount I'd say it's time to part company. If you really trust the mechanic then just give them the car or maybe you can find someone locally who wants a challange. A stuck valve is usually accompanied by some clacking menhanical noise of some sort. A warped leaking cylinder head would not usually cause any noise but would cause the engine to run rough depending on how many cylinders you have and how many are affected. Running short trips like you described (3 miles each way) is rough on an engine because it doesn't get warm enough to evaporate the condensed water inside the engine and it ends up getting mixed in with the oil which could cause all sorts of internal lubrication problems one of which could be a stuck valve. When this happens the oil on the dip stick tends to start looking foamy like chocoate milk. The engine needs to run at least 15 min to get rid on the condensed water. Also it's tempting in cold weather when making short trips to gun the engine after first getting it started to get the heat faster. This is not a good idea because the oil is not circulating as well and repid heating of a really cold engine may cause problems. Just let it warm up on its own.