Here is the completed story with the correct time expressions:
I woke up early last Saturday morning. I was really excited because I was going to Florida to visit my uncle. I didn’t want to forget anything! First, I packed my bags and checked the weight – no problem! Then I made sure I had my tickets and passport. Next, I called a taxi to take me to the airport, and five minutes later, it arrived. Everything was going perfectly, but then we suddenly hit a traffic jam on the road to the airport! By the time we got to the airport, I was really anxious. I hadn’t flown on my own before, and now I was really late. After I’d gone through the security checks, I only had ten minutes to get to the gate. Finally, I got onto the plane just in time, and was able to sit back and relax, and begin to enjoy my holiday!