Well, for people who have color blindness, it means that they have trouble seeing red, green, or blue or a mix of these colors. So you can just check your child with this evidence. And in common, color blindness is a genetically inherited condition. There are many reasons which can lead to color blindness. Some kind of eye problem, including injury of the eye, aging or as a side effect of using certain medications or drugs can be possible. For your child situation, you need to check if he gets inherited color blindness or not, for inherited color blindness will last forever and it can get worse as the time goes by. On the other hand, partial color blindness can be treated by wearing corrective glasses, surgery, or by quitting with consuming certain drugs or medications.
How old is your child? Does he/she know different shapes like round, rectangular, triangle? Can he/she count or know any numbers? If so, you can find pseudoisochromatic plate for him/ her. You can search"pseudoisochromatic plate" online. Just with several clicks, you can get a simple color blind test for your child.
The basic and easy way for you to check whether your child is color blind is to give him some colorful pictures with numbers inside and ask him the exact numbers. If he can say the right ones, he is not color blind. If not, he may be the color blind. However the scientific and right way is to bring him to the hospital and ask the doctor to have a check.