Do I need a sublimation printer?

Yes. Because of the fact that Sublimation ink is rather different in composition than normal inkjet ink, it requires a print head that can handle this and works without heat to prevent clogging. Also, special color management is needed to get the correct colors on the product as the print on paper is not the end result and changes significantly during the heat pressing process. Your best choice of printer is one that combines these things the best: Print head, ink and color management need to be perfectly balanced to get the best results.