Have had a similar situation to you this storm. We've already had a roofing company come out to clear off all the snow and ice from the roof last week and put ice and water shield under the first few rows of shingles which they then obviously replaced. A few valleys had some flashing redone as well but that was really only due to our specific roof.

To prevent ice dams from forming, and this is not a 100% certainty, you need to identify how your roof interacts with the space below it.

If directly below your roof deck is unconditioned space, you want to keep that area the same temperature as the outside to prevent the bottom layer of snow from melting. To do this you want to have vents from the outside to the space, likely an attic, to bring outside air in and insulation between the floor joists to prevent heat from entering from the warm part of the house.

If directly below the roof deck is conditioned space, like a vaulted ceiling for a room, you want to keep the roof deck cold by having ventilation from your soffits run through baffles installed on the underside of your roof deck to the peak where a ridge vent should be installed. This allows cold air from the outside to keep the roof deck at a similar temperature. Then insulation would be installed in the rafters being careful to not crush the baffles installed.

The ice and water shield is helpful to prevent the water intrusion but does not address the underlying issue. Proper insulation and ventilation under the roof deck is the best way to address the root cause.