I'm taking Taxol (paclitaxel) chemotherapy, my lips and skin are now drying out. What can I use to ease this problem?

Lips and skin. Pharmacists are, in my opinion, the best folks to help you select the best 'over the counter" creams for your lips and something else for your skin. If you decide to go that route please let me know how things are going.
Not pharmacist. Dermatologist. Use skin cleanser specific for dry skin such as Dove. Vaseline, Aquaphor, or chapstick will help your lips. A ceramide cream will be good for your skin, using several times a day, especially after in water. Eucerin eczema, Aveeno (oatmeal) eczema, CeraVe, generics, many others available OTC.