I also have chappy lips but not as serious as yours. I'm using an aloe chap stick that works pretty well. After I put on lip stick, I need to put on the chap stick to keep it moist. PM me your address. I can send you a sample to try out.
When it gets very bad, I also put vaseline on my lips before I go to bed. Drinking plenty of water also helps.
My lips also very easy to get dry, no matter summer or winter. some 潤唇膏 may not moist enough for me, so I used to put 潤唇gel. However, I tried a shiseido 潤唇膏, it works ok for me ... just $5 ... not bad. Also, last time when I went back to HK, I bought a mentholatum 有色潤唇膏 ... pretty moist ... unfortunately, I can find that in California.