For next time, there is an established Sierra Nevada method for digging in. If you have a tarp/shelter similar to a Betamid, you lay it out flat on the snow surface, then trace a line around that outside edge. Now set the tarp aside.
With your shovel and/or snow saw, you cut snow blocks out of the area within the line. The blocks are roughly 12 inches by 12 inches by 8-10 inches deep. As you cut them out, you set them straddling the line, half inside the line and half outside the line. You build up the snow block wall that way. After a while, you will have cut about two blocks deep into the hole, and those were used to build the wall about three or four courses high above the surface. The total of that is about 5-6 courses of depth, which is 40-60 inches from the bottom of the hole to the top of the wall. One end of the wall should be downwind, and the entrance walkway is left there.
Then take your tarp/shelter and begin to stretch it over the top of the wall. Assuming that you have ski poles, trekking poles, skis, or an old piece of tree branch, you have the choice of using them as center poles or roof trusses to support the tarp/shelter as a roof skin. That can be anchored down with the remains of the snow blocks. When finished, there should be floor room for two to sleep.