It is OK to use expired lip balm although expired lip balm may not be as effective as fresh lip balm but using expired lip balm will not harm you.
When your lips are so chapped even though you use lip balm it could be that your lips or yourself are dehydrated, you may have underlying health issues or the weather is too cold and affecting your lips.
Using too much lip balm can also cause your lips to become chapped and cause dehydration as lip balm can contain irritating ingredients such as flavoring and menthol.
Also licking your lips, sun damage, vitamin deficiencies and allergies to your current lip balm can also cause your lips to remain chapped even with lip balm.
Try drinking some more water, increase the humidity in your home or even add some Vaseline to your lips after you apply the lip balm which can help to seal in moisture.
Some chapsticks contain ingredients like menthol, camphor, or fragrances that can actually dry out your lips further, especially if you have sensitive skin.
If not currently using hydrating lip balm you should use hydrating lip balm with ingredients like petrolatum, Shea butter or hyaluronic acid.
Stay hydrated, avoid licking your lips and protect your lips from the sun with a lip balm that has SPF.
The lip balm that is the best and what I prefer is Aquaphor to the rescue which also works well for dry peeling lips.
Another good lip balm that works well is the Palmer's Cocoa Butter Swivel Stick lip balm.
Carmex lip balm also works really well and is a readily available lip balm.
Carmex contains beeswax which is an animal product so Carmex is not vegan and also contains Lanolin.
Other ingredients in Carmex are menthol and camphor.
The camphor and menthol give Carmex a cooking effect that helps to relieve irritation of dry lips and encourage a healthy appearance which feels good and looks good.
In some people that use Carmex allergic reactions may occur and appear as blisters, redness, or cracking of the lip's surface.
If you have an allergy to a specific ingredient in Carmex, then you should not use Carmex.
You can instead use Vaseline or other petroleum jelly to help seal in moisture and protect your lips when you can't use Carmex.
You can also put Carmex on your face and reduce the appearance of redness and help with chapped skin on your face.
Lip balm including Carmex is a good way to reduce skin redness on other areas of your body and not just your lips.