Hi Jennifer! For my money, the easiest way to do this, if you want to use the same wrinkles on many colors and you'd rather just paint them in and don't like the Overlay effect, is plain old Multiply and Screen.
Paint the shadows in black, and then set the Layer Blending Mode of that layer to Multiply, adjusting the opacity to suit the texture of the fabric.
Paint the highlights in white, and set that layer to Screen, also adjusting the opacity to suit.
That should do it!
If you want the wrinkles to show more of the color of the fabric, which is sometimes desirable, you can change the color of that layer to a darker version of the color (set the color to be the foreground color, select the layer, hold down the Shift key to constrain the color change to non-transparent pixels, and tap Option/alt + Delete.)
Or you can use two layers, with one set to the fabric color, and one to black, and balance the opacity of the two to suit. (Both should have Multiply as their Layer Blending Mode, of course.)
If you're working with a printed fabric, and you want to use all the print colors, make a copy of the color layer, (Command/ctrl + J) select the opacity of the shadow layer (Command/ctrl click on the layer thumbnail,) and then, with the copy still selected, click the Layer Mask icon to make the shadow into a mask. Then set the Blending mode to Multiply, of course.
Combine the regular Shadow layer and the colors to get the shadow you want. (Multiply won't affect light colors, so if your pattern is on a white background, you'll still need some shadow, although you might want to make that layer dark slate blue to keep them from being just plain gray.)
When you switch to a different color, just change the colors in the shadow layer (if you used them,) or make a new copy using the same mask for the pattern layer (if you used that.)
Personally, I prefer painting the wrinkles too; but I'm very comfortable with painting. A lot of the other techniques I mention here are for people who aren't, so they won't have to. But if you prefer to paint, then by all means, do so! I agree that you can get a lot more control (read; exactly what you want, with total control,) when you just paint it!
As has been mentioned before, there are dozens of ways to do almost everything in PS!
If anyone would like to see a different technique to do the same thing, just ask!

Ummm.. or you could just draw on the Overlay layer with white and black; but I find it better to split them out, so I can control the opacity separately, or use the color techniques.
Hope this helps!
Edited to add the bit about drawing on the Overlay layer.