I'm not the expert but here's what I did a years ago, drain all the water out of your system. There's a plug under your radiator somewhere and you have to unscrew that to drain your radiator. Do not open your radiator cap when the engine is hot or else the water will come rushing out and burn you. Fill it up with tap water first and let your engine run. Check for obvious leaks, fans working properly, while monitoring your temp gauge. Open your radiator cap and see if the water is flowing well or if its steady. The water should flow to indicate your water pump is working well. Feel your water hose if water is flowing too. Press the water hose repeatedly and see if water squirts on some areas, there should be no water squirts. If all seems well, drain the water and replace with distilled water and coolant in
1:1 ratio. Run your engine, and you need to bleed air out of your radiator. On my honda theres was a bleeder screw near the water hose, I open it until air no longer comes out and then refill my radiator with distilled water. In your case you might have to refill water after a few days of using your car, the trapped air may have already moved near the cap.
To be safe, keep rag towels and gallons of water in your trunk, in case of emergency, while you still monitor your temp.