Allergic reaction to hand soap or just dry skin?

I started a new job on January 2nd. About a week later, I was washing my face before bed and it felt as if I had a burn on the back of my hand, mostly along my thumb. The hot water felt even hotter as it ran over that skin. I then noticed that the skin was red there as well as the same spot on the other hand. I applied some lotion and it was gone in about a day. I didn’t notice it other than the sensitivity when I put hot water on it.

I noticed the redness again once after this, but yesterday it got pretty bad. It burned and itched and got redder and redder, spreading onto the backs of the rest of my fingers and even a little around my wrist. I applied lotion, which felt good at first, but made the area burn like crazy for about five minutes afterward. It eventually calmed down and stopped burning, but some of the redness stayed. Here is a picture of my hand yesterday at its worst.

Today it’s just got a little burn to it and the redness has decreased a lot, but is still there. I hear about “dry, cracked, burning hands” during the winter all the time, but I’ve never experienced it, so I thought that might be it. However, it doesn’t feel rough or scaly like dry skin – it feels completely normal to the touch. Then I started thinking about new products I may have come into contact with. I’m using new makeup products, but nothing that touches the back of my hand and my face isn’t broken out, so I doubt it’s that. The only other thing is the hand soap in the bathroom at work. I’ve never experienced any kind of reaction to soap on my hands (only on certain female parts, if you catch my drift), so I don’t know why it would happen now, or why it wouldn’t completely cover my hands.

I decided to go out last night and pick up some new hand soap to use (Silk Original Foaming Hand Soap) and hand lotion (Curel Ultra Healing Intensive Lotion). Whenever I go to the bathroom, I use that soap to wash my hands and I apply the lotion once I’m back at my desk. I hope this is enough to get rid of this, and I certainly don’t think it’s bad enough to see a doctor, but I wanted to see what you guys thought it looked/sounded like and if you’ve ever experienced it. Maybe you know of better products I can pick up to get rid of it. I was hoping to develop a tolerance to the soap at work, but I don’t think that’s going to happen.