Based on the limited information provided, it would make sense to have a landscape designer or contractor visit to determine if there are drainage issues involved and if so, make recommendations on how to correct.

Generally, what grows on persistently wet, poorly draining soils is algae. And that can have an effect on those with respiratory issues. Mosses or liverworts or other moisture loving species are generally not of concern.

You might have to improve the drainage. Do you have standing water?

And are you sure the problem is mold? I live in southern BC which is temperate rainforest. Everything is wet 9 months of the year here. Nothing that is exposed to fresh air and sunlight molds. Moss, fungus, yes. Mildew on wood fixtures, yes. Mold, no.

Other things that might be making you sick: radon, a noxious weed, hay fever, residual chemicals from neighbour's or your own gardening, particulate matter in the air from nearby mills, factories, or farms...

Have you been tested for allergies? I found out that I'm allergic to grasses and have to take Claritin and Flonase if I plan to be outside for an extended time or near lawn mowing.