While the problem is manifesting in your feet, the source of the problem could be elsewhere. For example, if you have an issue with dry skin generally, that condition will be exacerbated by the lack of humidity in your house that is typical at this time of the year. There are inexpensive devices you can buy to measure the humidity in your house - it should be approx 40 to 47%. If not, try using a humidifier. Likewise, people often have a harder time staying well hydrated in the wintertime. A good rule of thumb is to convert your body weight to ounces, then divide by 2. This will give you a measure of how many ounces of water to drink per day. For example, if you are 100lbs, that would mean you should aim to drink 50 fluid onces of water (not coffee, soda, fruit juices, etc.) per day.

Your chronic GI issues with reflux, gastritis, or inappropriate acid production in the stomach points to another source of difficulties for your skin, as does a hypothyroid condition and general effects of aging. You would also want to look at what kind of footwear you are using - different types of fabric/materials used in footwear (socks, shoes, etc.) impacts the ability of your feet to shed moisture. You would also want to ensure that your skin condition wasn't due to opportunistic pathogens, as in athlete's feet.

A naturopathic physician is a good source of information on all of the above. You could try a dermatologist, but they often simply throw corticosteroids at the problem. Another potential source of advice would be a podiatrist, but I would call their office first and speak to the clinical staff to see if they feel a visit would be worthwhile. Your MD could make a referral, which usually will get you a faster appointment.