Hi. Welcome to the forum.
It can take anywhere from a few hours to a couple of days in some cases before you see visible signs of fermentation. Just relax, and keep watching that airlock for signs of activity. Usually it'll kick in within a day, and your airlock will start bubbling.
Don't overfill the airlock. It should only be about half or slightly less full. Are you sure the water level is going down in the airlock? Do you see any cracks or evidence of a leak in your airlock? Does it look like water is being drawn into the fermenter? If any of the water is getting in your beer, there is a possiblity of infection. Then again, that could happen and your beer could turn out fine.
You definitely want to check that air lock for integrity. Pull it out and lay a bit of sanitized or flamed foil over the hole to keep dust from dropping into your beer while you check the airlock for problems. If it seems fine, just reassemble, resanitize, and replace it and stop worrying.
If you want to describe your entire brewing process, it might help us to understand your situation better.