I would not add chemicals to your tank. Think about it: Mother nature adds no chemicals to her water...she just keeps things in balance. Healthy balance=healthy tank.
How much gunk is on the bottom of your tank? Do you do gravel vac EVERY time you change water? Do you vacuum around and UNDER tank decorations. At least once a month you should lift and vac under all decortations. It's amazing how much gunk gets under there!!

How much and how often to you feed your fishy? Over feeding can lead to a huge algae bloom...
For a tiny tank like a 10g I would be doing at least 50% water changes every 5 days. Green water is caused by high nitrAtes, high light levels, high iron levels, overfeeding and high phosphates. I suspect that in your case it's high nitrAtes. Do larger water changes with more vacuuming. Reduce light times and if you have phosphates in your tap water, you can remove them with a phosphate inhibitor.
How large is your baby Suki(love the name)? Contrary to popular belief, I think it is nearly imposssible to maintain goldfish in a 10g for the 20+yrs of their life.
Think about it: once you add decortations and fish the amount of water in a 10g is actually closer to 7g or maybe 8g if not highly decorated. A 20g would be easier for 1 fish, 25g for 2 etc. Remember Orandas have the potential to grow to 12 inches. Could you imagine a 12 inch fish in a 10g? Pretty big...I wouldn't keep an adult goldfish in anything less than 25g per fish, but it can be done if you are willing to do the work.
I found it too hard to maintain nitrate levels at less then 20ppm( let alone the 10ppm that I strive for) in a 20g let alone a 10g. I upgraded to a 37g with plans to upgrade again to at least a 55g in a year for my 3.
Now then, that being said I think with increased water changes and better gravel vacs you will see a vast improvement. I can almost guarantee if you get your nitrate levels down below 20ppm, and keep them there the problem will resolve itself. It may take awhile, but it will happen. Do however many changes a week is required to maintain this.
I really don't like the idea of using chemicals or medications. If you take good care of your fish, and give them enough space, they will not get sick. Poorly maintained tanks are the reason fish get sick. A properly maintained tank takes care of itself.
Now don't take this post the wrong way. I am not saying that you can't keep a goldfish in a 10g, and I am not calling you a bad fish keeper.

I just think that in the future you will begin to have problems like I did. Hopefully it will clear up, and Suki will appeciate the extra clean water. So will you. You can never have too many water changes. Just don't change more then 50% at a time. I know a man who changes 50% of his 75g discus tank EVERY day. Can you say a lot of work!?!?!
A popular saying on another fish board I go to: " Fresh water fish like fresh water" Good luck! Keep us posted.