As far as general lip care, I can help you there! :D
In my experience, the only time I can remember having a similar state of lips (soft but tight) was when my lips were exfoliated and at the same time dry. Normally, when your lips are dry it may show "ashyness" or signs of peeling and dead skin cells. When you exfoliate your lips (scubbing the dead skin cells of the skin) you reveal newer, softer, and smoother skin. When this new skin becomes dry, sometimes it won't peel right away, but instead of showing dead skin cells, it will turn tight.
I exfoliate my lips weekly after my shower, and if I don't apply a good lip balm soon after, my lips will become really tight while remaining soft. A good lip balm usually restores moisture and elasticity.
1. Hydration
Are you drinking plenty of water? We all heard the "It's recommended you drink 8 glasses of water a day", but let's be honest, who really does? We tend to drink "enough" to satisfy us. Since the skin on our lips is a lot thinner, they are the first indicators of dehydration.
2. Dead skin cells
As mentioned, you can try exfoliating your lips weekly. A fast and simply way is to gently brush your lips with your (wet) soft toothbrush for a few seconds. You can also make a homemade lip scrub by mixing a drop of honey, and the same amount of sugar. Optional is a drop of olive oil. The sugar acts as an exfoliant, while the honey acts as a moisturizer, antibacterial, and sweetener. Olive oil is also full of antioxidants, vitamins, and also a natural moisturizer. If the mixture is too thick even with the olive oil added, moisten your finger with water before applying scrubbing your lips (scrubbing with toothbrush or rubbing with finger). Once done, just rinse with water. All ingredients are basically water soluble and will wash down the drain no problem.
3. Health Condition
Sometimes dry lips can be caused by a health condition of if you're on any medications (side effects). Since once again, I don't have too much experience with this part, all I can suggest is to see your doctor if you feel your dry lips are severe after trying the home remedies.
P.S.
You didn't really specify what type of lip balm you use. I know you said ChapStick, but ChapStick has many different types in it's line. Read the ingredients and pick out one that contain a list of ingredients that actually moisturize, nourish, condition, penetrate, soften, and smooths the lips. Petroleum jelly (Vaseline) is okay, but it does not moisturize the skin, it acts as a protective barrier from outside environmental damages while trapping moisture loss. This causes the skin to hydrate itself from the inside out.
Some common ingredients that moisturize the skin are:
olive oil, coconut oil, sunflower seed oil, jojoba oil, shea butter, cocoa butter, lanolin, vitamin e, petrolatum (skin protectant), beeswax (skin protectant)
These are common ingredients found in natural lip balms.
If I could make a recommendation for you:
1. EOS - This is by far the best lip balm I have ever tried. The coverage is very light (opposite from petroleum jelly) but I found the moisture it provides to be superior nonetheless. 100% natural, 95% organic. Has the flavor, and the scent.
2. ChapStick Naturals - Like I mentioned, ChapStick has several types. I find their Naturals line to be the best. Their naturals line has two types: Botanical Medley and Lip Butter. Both are nearly identical, except the Lip Butter contains a few butters such as avocado butter, thus making it a bit creamier. The Botanical Medley has a bit more candelila and carnauba wax (both natural waxes like beeswax) and so the stability is stronger and a bit harder.
3. My top recommended lip balm for the winter. It is petrolatum based with active medicated ingredients. It has a thick consistency making it great for the cold winter months. The medications help sooth and ease discomfort on the lips (pain, itching, soreness, extreme chapped). I would recommend the original jar formula. At first may feel a bit too hard and thick, but it softens up with use. It is easier to use during the warmer weather. You can also try the tube and squeeze tube version.
That's all I could remember to say for now....good luck for now :D