It's not clear to me how ice dams form on a flat roof. It must have some sort of pitch so a "dam" forms on the downslope side and prevents the water from runing off. Otherwise your problem is that a puddle forms in the low point in the center and leaks through (although I'd expect this to happen during/after significant rains also). Lastly your roof slopes back towards the main roof and leaks at the intersection. If you have "dams" that are actually blocking runoff, one suggestion is to fill a nylon stocking with ice melt pellets and rest it across the dam. The ice melt will slowly eat its way through the dam to the base roof and let the runoff out. If the sunroom below (and the cavity in the ceiling) is truly unheated then I can't see the insulation doing much for you. yopu actually want to vent that space so then underside is as cold as the top. Shoveling the roof sounds like the best short term corrective action you could take. Sheet roofing on flat roofs is supposed to be tight enough to withstand some ponding, but there still needs to be some slope (using crickets) and a drain mechanism. Pictures might add some clarification. Hope that helps.

I just made a long post to answer someone else's question about ice dams over on the Old House Forum. I'll attach a link. But your situation sounds slightly different. For first aid, I would take advantage of the slight moderation of temps and get up there and get the ice and slush knocked out of the gutters, ASAP. Start at the down spout point and clean up along the line to get past the point of blockage. A hair dryer can help, particularly if you have aluminum gutters. It won't do much to solidly frozen run, but to hasten the removal of slush it works OK. A flat panel paint burner can help, too, but takes some experience to avoid damaging the surrounding surfaces. With both these please use a GFI outlet to plug them in since you'll be awash in water and using an appliance at the same time. I would never allow anyone to use a torch to do this, though. Too dangerous. After the gutters are clear, and until you can make any necessary changes to insulation, slope of gutter, flashing, roofing or underlayment, etc., you will just have to rake the roof after every snowfall. It's not that hard to do. I always used to let my DH do it, but last year he was laid up so I found it could be done pretty easily. I was doing it on my second story this afternoon. The good thing is that ice dams seem to be an artifact of of early, unusually cold and snowy winters. Later on in the season the sun is higher and it's less of a problem. HTH, Molly Here is a link that might be useful: Ice dam question on Old House forum

Coffeemama - I’m not sure you understand the reason for the ice dams. We had ice dams this year as well with water damage too. Even with freezing temperatures, if the insulation under your roof is not adequate, the heat is escaping through the roof and melting the snow. We had a hard time finding a contractor. I had a list of 10 from Angie’s List and went down the list. Had a couple of tentative promises to come and then no shows. We finally got an appointment for 5 days after the initial water started leaking. While we were waiting for them to come, I just couldn’t watch water keep coming into the house, so we called a local hardware store where we had received reliable advice in the past. They advised us to try to rake some of the snow off that we could reach without getting on the roof. And to buy pantyhose and calcium chloride and fill the stockings with that and place along the gutters on the ice. We called a family member to come and help, who advised that we get a ladder ‘stabilizer’ to add safety to putting the ladder against the house. They were able to get up to the gutters and using a roof rake pull off some of the snow they could reach and place the calcium filled stockings. This stopped the water from coming in and it stayed that way until the roofers came and got up on the roof and took all the snow off and knocked back some of the ice on the gutters. This was on the back of our cape that has a dormer on the back, so the roof is two stories high. In the front where the roofline is only one story high, my DH and son spent 5 hours pouring hot water on all the ice along the gutters in the front. It is a two person job, one person on the ladder, one ferrying the hot water pitchers back and forth. It did work though. Completely cleared the gutter in the front of ice. We could have done the same thing in the back, which is what we would have done if the calcium filled stockings had not done the trick. We've had to stay on top of it and keep getting the snow off the roof and take care of too much ice on the gutters. If I were you, I would call my home insurance policy holder and ask them to advise. They certainly don’t want you to continue to get water into your home and might have access to qualified contractors.

Are the ice dams above the areas free of spray insulation? If so, the lack of insulation caused the heat from the building to form the ice dams. Adding the insulation to areas that already have ice dams will not remove the ice dams, only melting the ice from above(warmer weather or physically melting) will remove the dams. But, once the spray insulation is installed, new ice dams should not happen. Ice dams usually occur with incomplete insulation/venting problems. Warm air from inside the building melts the bottom layer of snow on a roof, which flows down the roof surface to a colder section which freezes at the eaves/edges of the roof. That builds up over time to cause unwanted ice buildup. Freezing rain causes buildups of ice that looks similar, but covers everything, not just eaves/roof edges. There will be a layer of ice on the entire roof, trees, power lines, plants, everything. Icicles form with normal thaw/freeze cycles during the day/night when the sun heat begins to melt the top layer of snow on a roof, which flows down and freezes as the water drips off the edge of the roof. Incorrectly insulated/vented attic spaces can create a combination of ice dams and icicle buildup. Different situations that can seem similar. The solution is to determine if the building is correctly insulated and ventilated. In your situation, freezing rain seems to have caused the problem, unless it happened on the yet to be sprayed areas.