No, you'd better not wear the contact lenses when you have the serious stye. Or else, your eyes may easily get infection and cause the bacterium in the eyes. You must not wear the contact lenses. If you wear, you may get many eye problems. You should firstly treat your stye and wait for the recovery and wear it. You need to protect the eyes carefully.
No, absolutely no.
If you are suffering from styes, when you wear contact lenses, you may feel painful. What's worse, when you are wearing contact lenses, the stye recover more slowly as your eyes have less access to oxygen. The blood circulation in your eyes may be slowed down. Last but not the least, the bacteria, dirt and protein from your contact lenses may worsen the situation of your styes.
The best thing you can do is take off your contact lenses to conduct a good recovery condition for your eye stye. You must know that eye stye is usually due to infection, any infection can lead to it. Bacteria, injury to eyes and allergic eyes are all causes of eye stye. Wearing contact lenses only can prolong the recovery time of stye. That is for hands obtain too much germs and virus invisible though you though you have already wash them up. And when you wear contact lenses, you need to put them into eyes by hands. So you just create more chances for them to get worse your eye condition. Warm tip: wear eyeglasses may be your best choice during your stye.
As far as contacts go, there is an infectious/inflammatory process occurring in/around your eyes, so it's best to not wear the contacts...you could end up with a corneal infection. See your eye doctor to resolve the issue and get an updated pair of glasses--never know when you'll need them.