Sea ice doesn't contribute to sea level rise when it rises; continental ice sheets and grounded ice shelves do. There are three great ice sheets: West Antarctica (~2.2 million km³), Greenland (~2.8 million km³) and East Antarctica (~20 million km³). By contrast, the largest ice shelf, Ross Ice Shelf, is only ~0.1-0.2 million km³. I don't know how much of that is grounded and thus capable of inducing sea level rise on loss. By comparison, the piece that's breaking off is only 1700 km³ or so.
Our knowledge of the exact state of these ice sheets and shelves has a lot of holes in them, but it's clear that the East Antarctic Ice Sheet is gaining in mass, West Antarctic Ice Sheet about stable to slightly negative, and Greenland is shedding at a fast clip of a few hundred km³/year. The ice shelves, particularly in West Antarctica, do seem to generally be in retreat.
At current rates of loss, the melting of the ice sheets provide only a very modest rate of sea level rise--maybe 0.5mm/yr. By comparison, in, say, Norfolk, the isostatic rebound from the loss of the Laurentide Ice Sheet contributes about 1.5mm/yr in sea level rise. The fear is that there could be some kind of tipping point that causes the ice sheets to very suddenly and dramatically collapse (à la Larsen B), but we don't have much evidence to suggest that this is likely to happen.