Well made custom ICC profiles will always make your prints look their best. Check where you got your ink from, they may offer a generic one for your printer that will help.
Also 100% polyester substrate will have much better color.
Some of your print (on the shirt you described) will wash out in the laundry.
Your colors dont look bad for no profile and the wrong fabric. Dye sub is really for polyester or mostly polyester clothes. Cotton doesn't really work for it without using other products.