I agree with the potential allergy idea - coating the clamps wiht wax or getting rubber tipped ones may help.

The problem you are likely to come across is pain from ischamia reperfusion injury. Thats where an area of the body has been deprived of blood flow for a length of time and is suddenly released and has blood flowing back into it. The shock of the blood flow can be painful and as damaging as the loss of blood in the first place. It is common in stroke victims (when the clot shifts or is removed by surgery) and in accident victims with a crush injury (which is one reason why first aiders are not supposed to remove anything crushing a part of the body if they suspect it has been there more than 15 minutes - the reperfusion can kill the person or do irreperable damage).

In the nipples it is generally a lot less serious than it is above but you do need to be careful and ensure that the nipples are not clamped tightly for too long (usually 15 minutes). IN fact, most people tend to be real cruel bastards and clamp for 15 minutes, take off the clamp, massage to get blood back in there which causes more pain, then reclamp for another 15 minutes... rinse and repeat

Too long clamping can cause blood vessel damage and nerve damage if you are not too careful.

I've always found that the pain of clamping usually goes mostly away after a nice warm bath - it helps to reperfuse the tissue and sooths the grazed skin. Add some lavender oil (10 drops of pure essential lavender oil) to the bath as well as it helps to relieve pain and relax tense muscles which can exacerbate pain.