I've picked up goldfish many times, always with wet and clean hands (usually to move them or during emergencies, etc.). Expressing eggs out of a female is another thing all together. If you don't know what you're doing, you can cause the fish severe damage. If she is egg bound, that means the eggs have started to rot and bacteria are growing. At that point, you can't express her eggs anyway. That can only be done with a healthy female who is not egg bound but ripe with eggs.
I assume that you have her in a pond with males or is she an aquarium fish? If there are males with her, the chances that she would be egg bound are very remote. It's more likely that she has an internal bacterial infection such as dropsy or tuberculosis or perhaps has a problem with her kidneys (fluid retention). See this section on my site entitled, "Why is my fish fat?"
http://www.fishpondinfo.com/health4.htm#fatNo matter whether she's egg bound or has some other sort of infection, antibiotic injections would be her best chance for survival. If not, then you can try regular in-the-water antibiotics. Depending on her problem, they may or may not help. In any case, the addition of pond salt will help her deal with infection, fluid retention, or whatever the problem is. In a pond setting with plants, a 0.05% solution of sodium chloride is fine. If you bring her into an aquarium or that's where she is, then you can double or even triple that amount to have a greater treatment effect. You can also treat her with magnesium sulfate (epsom salts). What exactly they do, I'm not completely clear on. You can search for epsom salts and goldfish or koi on the internet. Here are some discussions I found on it:
http://www.kokosgoldfish.com/forum/lofiver....php/t5578.htmlhttp://www.koivetforums.com/forums/showthr...p?threadid=7118