Yep. You tend to keep your mouth open and that makes the lips dry, or you lick your lips. Use chapstick.
Cold Sores w/ Braces. Cold sores- technically a herpes simplex virus lesion, have nothing to do with orthtodontic appliances - unless that brackets or wires are causing lip trauma or abrasions, which could incite an hsv outbreak. As far as lip dryness is concerned, chapped lips can also sometimes incite an hsv outbreak, so can stress hormonal changes, sun exposure, etc. Keep your lips regularly moisturized.
Having very dry lips from past 2-3 weeks, drinking enough water. Have orthodontic braces and undergoing some course of antibiotic from past 4 days. Help?
Not from braces. Dry lips can be from mouth breathing (especially if nose clogged), licking lips and causing them to chap, medications, change in diet, allergies, etc. Try using a lip balm such as Chap-Stick, or put Vaseline Petroleum Jelly on your lips. If it doesn't clear in a few days see your General Dentist, Orthodontic Specialist, or Primary Care Physician for further examination.