The red color in your eyes occurs due to dilation of small blood vessels (these are the small red lines) in the white part of your eye.
This can often occur from irritation of the eyes. The most common reason to have irritated eyes is because of eye allergies. Eye allergies are called allergic conjunctivitis medically. Many people with allergic conjunctivitis also have nose allergies (allergic rhinitis) which causes stuffiness, runny nose, and sneezing.
There are many causes of allergic conjunctivitis, including smoke, dust, pollen, dust mites, pet
dander, and other things.
You should go see you pediatrician
as soon as possible. They will be able to take a look at your eyes and help you figure out what is going on. If it looks like allergic conjunctivitis, then you will need to think about avoiding the things that are provoking it (such as pets). Your pediatrician may also prescribe you some medicines to help with it. If you do not think that you want to use eye drops, then it is possible to use some oral pills. For example, antihistamines like loratidine (Claritin) or cetirizine (Zyrtec) can be very helpful in reducing the redness and itching caused by this condition.