Visa

Your real question should be, am I eligible for 24 hour visa free transit?

If your entire transit time in China, calculated from your first scheduled arrival, in your case in Guangzhou, until your last scheduled departure, in your case from Wuhan, is less than 24 hours, you will be eligible for 24 hour visa free transit and you don't need any kind of visa.

You will print out your flight tickets and have those printouts with you. Also, you will declare at check-in in the Philippines that you will travel to US via China using 24 hour visa free transit. After a short inspection of your tickets, you will be allowed to board the plane.

Upon your arrival in Guangzhou, you will approach 24 hour visa free transit counter where you will apply for a temporary entry permit. This will allow you to travel through the next segment that will be a domestic flight. In reality, this is not so complicated at all.

All you have to do right now is to check whether your transit time through China will be less than 24 hours. If this is the case, you are eligible for 24 hour visa free transit and you will travel through China without a visa.