no heat except for first few seconds then blows cold air

Your recent repairs do not appear to have anything to do with the cooling system. I would check engine temperature to see what it is when the engine is warmed up. If the engine temperature never seems to get as high as It should go (nearing 200 degrees and beyond when hot), then you could have a thermostat that is sticking open. Sure, flush the cooling system, but I don't suspect you will have a concern there. Always be sure to purge the cooling system of any air after cooling system repairs. www.repairpal.com/repair-shops