Your photos didn't load but I was able to copy and paste and view two of them. That soil looks high in organic matter so much of that mold may be some fungus that's enjoying the warm, moist enviroment and helping to decay some plant matter.

But I would be very concerned because those plant stems look pretty thin and that same warm moist environment is perfect for the development of damping off fungus, in fact it looks like you may have lost several plants to it already. It can wipe out all your young plants very quickly if left unchecked. I would definitely dry that soil out and get some better air flow.

When I suspect damping off fungus is starting to appear in my own plants I spray with a fungicide for rapid control, but I know some people like to avoid chemicals, particularly in the home.

Without the fungicide, how can I get rid of it? The weather here is off, so I'm afraid to put them outside just yet. I'll be scraping off the top soil and drying it.

All of our plants will be going outside as soon as the weather starts to look more predictable. Unfortunately, Texas weather is moody and not very consistent until Summer, haha.

Thank you so much for the help. (: Is there any other advice you could offer?

The way to get rid of it is to change the conditions from the current one that fungus thrives in, to one that fungus hates. Crowded plants, high moisture levels, no air flow are all conducive to fungus. So you want the soil and air much drier, maybe set a fan up to blow air across the plants to get rid of the stagnant air around the plants and bring in fresher air. Not crowding seedlings is also key, but that's easier done by planting seeds well spaced when planting. You could cut out some plants now but that's risky since you don't know which ones have the disease for certain. You could transplant to spread them out, but they look a bit small for that. Maybe someone else can suggest a treatment for damping off that doesn't involve fungicide?

My window is usually open, but recently bees(although I love them!) have decided that my room is a wonderful place to crowd and then slumber. That, and it's been too cold to keep the window open.

I do know of a couple people who have a fan I could borrow until I put the plants outside, though. I can also at least separate the pots from each other. The package that I bought said to put in four-six seeds, so that's what I did. I guess that wasn't a good idea, ha.

Hopefully these plants make it and I can separate them soon. If not, it's alright, as I have a ton of seeds left, but it would still be sad.

Mis some 3% hydrogen peroxide and water to 500-1000 ppm.....use it to water your plants.

Get a fan and use it.

Just wanted to give everyone an update.

I went ahead and replanted them. I lost one so far, but the others seem to be doing well. I'm watching them all closely to make sure they don't get anymore mold or anything like that. Got a fan. Tomorrow, I'll take pictures and post them(and hopefully they'll show up this time).

As promised, here are the pictures: