Subdivide Artifacts (look like thorns)

I’m getting these artifacts with subdiv on. They are created whenever I create lines between 2 points with CTRL-F. How do I fix this? Thanks in advance!

EDIT: I took the subdevide off and I see that its a problem with there being geometry with unmarked edges created inside the lines i’ve already made. No idea how to fix this. i tried dissolving the faces with unmarked edges and deleting them but it didnt work: probably because that’s not how you fix this. Thanks for the help!

Turn off the modifier and go and actually look at the mesh in that area.
Move a vertex, see any issues.

Things to check.
Remove any internal faces
Remove double vertices
Use only 4 sided faces on non planar surfaces

You haven’t included a link to a blend file to check. WHY ??? Please ALWAYS DO .You’re just making it 100x more difficult for anyone to help you.

Appologies. Here:

You need to watch your modelling. Triangles and faces with > 4 faces are bad with subsurf. You don’t also want poles (verts with lots of connected edges). This will lead to pinching and difficulty to control a clean mesh (example with the antennas) Ideally you want edge loops going around their base

Delete those faces and rebuild your mesh

A quick rebuild but you would also need to fix a lot more.

Go watch some topology tutorials on youtube or cgcookie

Thank you so much, it looks way better now. So about the poles: no more than ~5 edges/lines per point?