You may want to pull the engine. If the ones on the side pushed out its a good chance the ones in the rear of the block also came out.
To install new ones the holes should be cleaned,,a socket that fits tight as possible will work.I have a aluminum plug that fits inside and drives the shoulder. Use a good sealer. DONT REUSE and make sure there brass or SS>
I would also pressure test the complete package sounds like you still had some water in the block.I have never seen freeze plugs push out without other problems.You might get lucky but a little time will save plenty $$$ and pain done the road!!! Good luck .
I use a electric heater in the really cold periods,some use light bulbs but to much trust in a bulb going out for me.