Nah, that's just carbon dust from a new filter. It's common and harmless, but you gotta flush it out.
Discard the first three full pitchers of filtered water after installing a new filter. You can use that water for plants. Just run it through the normal cycle and pour it out.
If the weird taste persists after three pitchers, your filter might be old. A standard Brita filter is good for 40 gallons, and a LONGLAST is good for 120 gallons. If it's been longer than that, replace it. Also, only ever use cold tap water (between 32°F and 85°F). Hot water can damage the filter.
Heads up: For the best taste, pour tap water onto the side of the reservoir, not directly on top of the filter, and let the water filter completely before you drink any.