Breaking out on your lips might indicate an allergy to something in one of the chapsticks.

I have been using carmex, since it has lanolin in, you can buy lanolin on its own and its meant to be very good, in the US I believe it is the same thing as bag balm.

When dealing with dry lips I've found honey and sugar scrubs help, as you need to get rid of the dead skin before you can moisturise the rest. If cracking is a real problem I would talk to your Dr about a hydrocortisone cream/gel or something.

I've had really good luck with exfoliating my lips with my toothbrush every time I brush my teeth. Then I immediately apply Aquaphor. At night I do this same routine, but also apply Bag Balm along with the Aquaphor. My lips are super soft in the morning.

I use Bepanthen every night, i use LOADS of it. It looks a little white so not great for during the day but i find it keeps the serious dry lips at bay and i just use a normal lip salve during the day.

Or you can try Dr. Dan's Cortibalm. It's awesome but you can only use it a couple times a day because of the cortisone. I use Aquaphor and Lanolin as well (I've been warned that many people are allergic to lanolin though, so just be careful). I got Dr. Dan's from my derm when my lips were particularly shitty and I only use it occasionally. It heals them really quickly and then I go back to just my Aquaphor. You can ask the pharmacy to order you Dr. Dan's, they don't sell it on the shelves but you don't need a prescription or anything. You can also get it from Amazon.

Thanks for the replies!

Try exfoliating your lips gently with something slightly abrasive like those exfoliating gloves from The Body Shop and then apply a VERY thick layer of carmex. Do this every day