I can't tell you weather or not to put the CS in your eyes but I will say that I was a contact user as well and I frequently had this kind of pain when I overused the contact lenses.

I don't know if it was the same pain you're feeling or even caused by the same thing but when I used to do stupid things like fall asleep with the lenses still in cause I was too lazy and tired to get up and take them out, I remember the horrible feeling in the eyes when I'd wake up with them still in and this discomfort would remain for most of that day. It was even worse if I'd fall asleep with them in, and have to work or go to school the next morning so I'd take them out and put them in their case with solution to try and relubricate them for about one hour while I'd be getting ready to leave then I'd stick them back in for the day. The pain would be even worse throughout a day like that, it really sucked. Even a day where I would simply wear them too much would cause some slight discomfort, like say I'd put them on really early like 7am and only remove them at around 11pm right before going to bed. I also noticed this kind of pain if I'd keep a monthly pair of contacts for over a month. If I were to go back to contacts I would definately get daily ones. I was so dependant on my contacts and I know I really abused my eyes badly, I really regret it now..

I really think my pain was an eye strain issue cause by overworking the eyes (or rather over using the contacts) and not giving them much chance to breath, rest and recharge, and perhaps this is what you're dealing with. In any case I would suggest limiting your usage of them and try taking them off any time they're not absolutely needed. I haven't worn contacts in about a year now and only wear my very first and only pair of glasses if I really need them to watch tv or something and my eyes feel alot better to say the least. I don't know how bad your eyes are so this may not be possible for you but give your eyes a good rest and I'd think that pain should wear off.