Yes, I believe that it's possible (and wise) to self-disagnose on the Internet for certain ailments. If you have something really specific, you can probably hone in on it on the Internet. Now, if you're coughing, you should see a doctor. That could be anything. But if your jaw is hurting, for instance, you might have an issue with your muscles or something and the Internet can help you figure that out.
Yes, It is wise to self-diagnose via the internet but to not go to your doctor after for treatment would and follow up to what you think might be happening is a mistake. You are not a doctor therfore can not be sure what the computer says is going to be correct. Always do a follow up.
I believe it is important for people to understand as much as possible about their health and talk about that with their own doctor in person. It is far better to educated and you can educate yourself by looking for information on the Internet. The savvier you are about a subject, the better off. Be open to what your doctor has to say, but also remember that they're human and fallible as well.
No it is not wise to self-diagnose via the internet. You will think that you are dying and have many diseases if you do this. It can lead to you becoming obsessed with being sick and ill all of the time and inuries are more prone to happen because of the internet.