You needn't worry your eyes, even it will be red for a few hours. Firstly, you can use some eye drops which would make you feel well. Also, you can flush eyes with lots of water. However, If it does start to hurt or your vision becomes cloudy or disorted, then you should go to see the doctor for help.
A bug in your eyes typically would do no harm to your eyes as long as it take it out immediately after. But if the bug is aggressive, then you should be careful. Just try to flush it out of your eyes with normal saline, then get yourself some antibiotic eye drops to relieve your problem. It is ok, take it easy.
You should better get the bug out of the eye by using the finger. You should do it in front of the mirror which could help you see clearly where the bug is. You should do this in gentle movement in order not to break your cornea. After taking the bug out of the eyes, you could use some eye drops to release the symptom and make the eyes feel comfortable.