Car overheating and Heat/AC turning on and off

I drive a 2005 Hyundai Elantra. I have had this same issue before. Here is my best description of what is happening. As I am driving if I am going below about 35 mph or am stopped in traffic the temperature gauge on my car starts rising until it is in the red zone. At the same time it kicks off my air conditioning or my heat, which ever I am running. Once I start moving again and get to above 35 mph my ac or heat will come back on and when it does immediately my temperature gauge will drop back down to below the half way point. Not only is this a pain because I can’t stay cool or warm inside my car but I am really starting to worry about my engine overheating.

This same thing happened last spring. At the time I needed an oil change and when I picked my car up the gentlemen that did the oil change told me my antifreeze was low so he had refilled it. I’m not sure if he did anything else like flushed it out. However I quickly noticed afterwards my air conditioning no longer gave me problems and my temperature gauge stopped rising as well.

Therefore this time when this started the first thing I did was add antifreeze to my car. I was able to see when I did that that it wasn’t up to the fill line so I am guessing it was low. However when getting in my car today I noticed it didn’t seem to fix the problem, the ac is still kicking off and my temperature gauge is still rising. What should be the next thing I look into? I am far from a mechanic so if needed I will get it checked out however if there is something I can do first to perhaps fix or identify the problem on my own I would like to give it a try since money is a bit tight at the moment. Any ideas on what the problem could be or what I should do?

@parkersmom7108
"Therefore this time when this started the first thing I did was add antifreeze to my car. I was able to see when I did that that it wasn’t up to the fill line so I am guessing it was low."

Since you could see a “fill line” I’m guessing with probability that you are adding coolant to the reservoir container. I’d say that depending on what is wrong, filling there is NOT filling the cooling system, which I would guess is low.

There are quite a few reasons for low coolant problems, some easy and inexpensive to remedy, some not so much. You could have a leak (internal or external), thermostat, or cooling fan issue.

One thing for sure, if the car is indeed overheating, then by operating it in this condition will make any situation worse and more costly, putting the entire engine a risk.

It needs to be put into the hands of a competent mechanic/diagnostician for some inspection and testing and it needs to happen sooner (ASAP), rather than later. Keep your fingers crossed.
CSA

Sounds to me like your water pump is going out.
All water pumps have a weep hole, when an internal seal fails, coolant weeps out this hole. Can easily go unnoticed, and over time will drain the coolant system.
Could also be a bad head gasket or cracked head, letting coolant leak into the combustion cylinders, essentially hiding your leak, because your coolant is being lost out your tailpipe, as steam.