Hi Molly.
Any growth on or under the graft should be removed..You'll note root stock has a ton of thorns..By leaving them on takes energy from the main plants/s..So, if this sudden burst of growth was on or under the graft line, it's best you removed them..they shoot out much faster than the trees themselves..But your citrus sounds fascinating..
Mollie, where did you locate the Fruit-cocktail tree? I'd love getting my hands on one, even though there's a ban shipping citrus trees from Fl..Do you know of a site that sells these trees?
Citrus fertilizer works best..Since you're in Fl, they should sell it at your local nursery or hardware store..If not, there's a few online stores that sell Citrus fertilizer. Even Ebay sells it at good prices..Toni

Thanks Toni- I bought the tree at Wal-Mart. A 10 gal fruit cocktail was $100 about 2 years ago. I just saw one in July at WM, a 30 Gal for $135. Mine has been in the ground for 20 months and has about 20 growing fruits mostly lemons and limes here in its second year. A few grapefruit, two honeybelles and one naval orange. I'm not sure what on or under the graft line means but I think you are saying as long as the shoot is inside the good graft branch line, its OK and using thorns as a guide is a great idea. The lemons seem to have most of the energy. I dont know if I should prune the tree to equalize the energy in the grafts or just let it go on its own minus the sucker shoots. Thank again for your response, Mollie.