Leave it in Illustrator. Do all your work there. When you put it in photoshop it is rasterized. Png it self is a raster format.
Vector formats are ai, eps and pdf. Eps is not used much any more except for when needing to import into older programs. As it lacks a lot of features that ai and pdf have.
When exporting to pdf make the ai embedded into the pdf, to make it editable later in illustrator.
If you need to use a feature that can only be done in photoshop, it would be best to ask the printer. Only they can tell you how they can use raster effects.
I did about 40 t-shirt designs all in photoshop. What can I do now to print these the best way I possibly can on T-shirts at this point, while still getting the appropriate colors?
I also didn't use Illustrator because I don't know enough about it. I like to use the gradient tool and the paint bucket tool.
Yeah, illustrator can take some time getting use to. Especially if you never used it before. Illustrator does have a gradient tool but what is better is the blend tool. As each shade is an individual object. However that can choke some printers.
The paint bucket tool is really nothing more than a fill tool. But can be easier for beginners to use that haven't learned all the shortcuts yet.
Some prefer the gradient tool in photoshop over illustrator, but I personally think it is more what you are use to using.
There are features in illustrator that are raster based like the drop shadow for example. Which would cause an issue with any printer that wants vector only.
You could import your photoshop image into illustrator and let it auto trace it. It might create a viable vector object. Just make sure you expand the trace when you are satisfied to make it a true vector object. Problem with auto tracing is that it can generate an unwielding amount of vector paths, that are really hard to figure out if you need to fix it. But it will be a vector object that is printable as long as it doesn't choke the printer.