I was recently told by my mechanic that the new radiator coolants do not simply become ineffective as it ages, it becomes thicker and will clog your radiator and heater coil. This may have been what you are experiencing. Regular flushes of the cooling system are now imperative to prevent system failure.
Two things to check for simple fix. 1. Is the transmission fluid at the correct level and in good condition? Is the color of the fluid a clear, light red color? 2. Examine the engine and transmission for loose or damaged vacumn hoses. Both of these can cause hard shifting. You could of course take the car to a mechanic who can connect diagnostic equipment and tell you exactly what the problem is. Transmission problems rarely fix themselves and the earlier you do something about it, the cheaper the repair.
Does it do it when the engine is accelerated ? If so, the belt is probably slipping. Check the tension and tighten if possible. Alternately, get a product called Belt Dressing from the auto supply. Spray it along the inside of the belt while the engine is running. It will make the belt less slippery and less prone to squeaking.
You still may have an ice blockage further up the reservoir. I had this happen to my fridge once. I just left the door open for a couple of hours and it cleared its self. Use blankets over the opening in the fridge or freezer side to keep the cold air in while the door is open.