Hi Steve! Congratulations on the immersion into Photoshop.
There are a lot of ways you could tackle the star roundness topic. Re-creating the stars digitally like Norme described, and I'd never thought about the de-blurring method Pete described—that sounds really interesting.
Personally, I prefer just a balance between rough stars and perfect stars in my sketches. Sometimes if the stars get too perfect, the drawing seems to go a bit flat for some reason.
Here's a possibility to try:
Make a duplicate layer of your sketch (so you have 2 of the exact same drawing on 2 layers)
On the top layer, run the Dust & Scratches filter and adjust the Radius and Threshold to get some decent results on the smaller stars
- Radius will increase the effect of taking rough edges off the stars--but don't go too far or it starts to erase the smaller stars.
- Threshold sets a limit to what is considered a defect and as you raise it higher, it maintains more and more of the paper texture.
I tried Radius = 2 and Threshold = 8 on your drawing and that seemed like a good starting point.
If the Dust & Scratches filter smooths out your nebulosity too much, you can bring it back by adding a layer mask to your top layer and hiding the top layer around the nebulosity so the unfiltered, bottom layer shows through. (if you're not ready to jump into layer masks yet, you can also just use the eraser tool on your top layer to allow the bottom layer to show through)
The only thing left is dealing with the larger stars. You can use the clone tool (set to be a slightly soft brush) to paint paper around the elongated edges and manually round them out a bit. Or you could totally clone the big stars out and replot them entirely from scratch. (Only the two brightest stars in your drawing needed that extra bit of touch-up.)
I hope it's ok, I've attached a version of your sketch with those steps applied to it. It may not get the stars as round as you'd like, but it's something you can adjust to taste.
I've got as a to-do, that I would like to make a video of that process in action...hopefully I can work that up before too long.