What's is wrong with my car?

I have a 1998 Honda Accord EX and my car is overheating. It was running fine before the winter storm in Louisiana that caused temperatures to drop as low as 15 degrees. I started my car every day to make sure that it was still working. The water in the coolant reservoir was frozen but eventually thawed and I put more water in. I started my car up and went to drive and saw my temperature gauge rising to hot so I pulled over to a gas station and waited for a while then started it back up and put my hazard lights on then went home. I waited the next day then started it back up and went around the block it was fine for like 5 minutes then the gauge went up again but when I slowed down and braked, it dropped back to normal then rose back up again. So I opened to see under my hood while my car was on. The fans were not moving at all. I don't know if I have a bad water pump or a bad thermostat. I really don't know.

Try thermostat first because it determines on when your fan turns on or off

You need coolant not water for your radiator, hence the name "coolant".

Buy a new car

Obviously, your 20-year-old car needs the personal attention of a reasonably competent mechanic. Why don't you go find one.

First thing i would do is just make sure its got enough water in it .fluid in the reservoir doesn't necessarily mean the system is full. Make sure the motor is cold when you check it don't burn yourself.

I would change both.

Take the coolant reservoir cap off and fast idle the engine for 10 minutes or so, or until it reaches normal operating temperature. Check for bubbles in the reservoir, topping it up if necessary. Sounds like you have air in your system.
Either that or something is still frozen. To freeze in the first place your coolant mixture must have been too weak, it should have taken 15f with no problem

Chances are that when you started the car with the coolant frozen you wrecked the water pump. The blades are plastic and they are designed to pump water not ice!

Alternatively, if you are lucky you have an airlock in the system - it needs bleeding to get the air out.

When you get it fixed get some anti-freeze in the coolant. As well as preventing the coolant from freezing it also contains corrosion inhibitors that stop your system clogging up.

If you started the car with frozen coolant, that CREATED the problem. If you didn't have a coolant mixture that would stay liquid in temperatures below whatever you had in your area, you need a CLASS in basic vehicle care before you drive ANYTHING in ANY weather.

Consider it a GIFT if the water pump AND thermostat are the ONLY things you need to replace.

Overheating is caused by a lack of circulation. Find out why it isn't and fix that problem.