I recently felt the need to carry to a family gathering (long story). But when I was there, sitting on the couch, with little children climbing on me and pressing next to me, I couldn't get my mind off where the muzzle of that .38 snubby was pointed. It really kept me tense. It was in a good hard leather IWB holster, but it still freaked me out a bit to have it an inch or two away from a small rambunctious child bumping against that hip.
I wanted to comment on this, and you are probably already aware of what I'm going to say, but I just want to make sure.
If you are carrying the gun in a well designed (most holsters you'll find are) that covers the trigger, there is no chance of that gun going off. I have a rambunctious 3 year old, who likes crawling all over daddy. I carry my chambered Glock in an IWB leather/kydex hybrid style holster, and I have absolutely no fear of the gun going off because the holster retains the gun well enough I'm not worried about it coming out, and it would be impossible for the trigger to be pulled.
I understand your fear. I had the same fear. But I got over that fear with a combination of the thing I mentioned above, and training. Now, I would not feel comfortable carrying a gun without a round in the chamber. I think I take it even a step further than you...I picked a Glock specifically because it doesn't have a safety I have to sweep off (trigger safety doesn't count as it doesn't require an extra action to use). But that was my preference.
Do what's comfortable to you, but really, I urge you to learn to get comfortable carrying with a loaded chamber. Get some training...I bet there are several organizations that will do defensive handgun training. That will get you more comfortable.