The electric chairs that are still used today are a lot safer and more reliable than they were in years gone past. Today if you were to be executed in the electric chair you would probably feel very little pain, as the initial voltage of 2000 volts is used purely to stop the heart and to render you unconscious. After around 20 seconds the amp is lowered, and the remaining shocks will burn and damage all the internal organs, effectively making sure that the inmate is dead and cannot be revived.
That is in theory anyway. There have been multiple accounts as recently as present day of prisoners surviving multiple attempts to stop their hearts with the first dose of electricity. As some humans have more of a resistance to electrical currents than others it seems, not everyone is finished by 2000 volts on the first attempt. This has led to calls for the electric chair to be banned and for critics to have called it a cruel and unusual punishment. Which of course is banned in the Constitution.
There have also been problems where live inmates heads have caught fire, or where some of the electrical equipment has failed during use. Meaning the inmate is left badly shocked but not yet dead. At times the blood vessels under the skin have been badly burned and the inmate on fire while they are still screaming to be released. This has created problems for the state because it is surely cruel to badly damage a prisoner, only to have to keep him alive in constant pain until the chair is fixed during technical problems.
All this had lead to a decrease in the use of the electric chair, to the extent that now only 6 states use it on a regular basis. Those states being Alabama, Virginia, South Carolina, Florida, Kentucky, Tennessee. The other states that still use the death penalty having switched to generally only using the lethal injection of as chamber as choices for the prisoner.
So it is quite possible that you do feel pain from the electric chair, at least for the first few seconds. The first session of 2000 volts takes the full 15 seconds to fully stop the heart ad render the inmate unconscious, so for all that time you are feeling the pain of the current as well as the muscle spasms which accompany it. If the chair is faulty somehow, or you survive consciously the first dose of electricity, then you can expect to be cooked alive as the lower amp current burns all of your internal organs. This would be extremely painful and still happens enough that use of the electric chair looks to be discontinued altogether before much longer.