I am a full-time fabricator. DO NOT USE THESE ON YOUR CAR. I don't mean to bum you out, but they will not be safe. I am all for fabbing up custom parts, but this should not be your first project by any means.
First off, it doesn't look like you removed the paint around the weld. The paint burning will contaminate your weld. There is no way in hell a flux core should be used for this. IMO flux core is for artwork type welding only. These should be TIG welded and braced by someone who knows what they are doing. I would only half trust a MIG with the proper shielding gas. You're trusting 2000 pounds (plus the forces of driving which will be way more) on a couple of improper welds.
Again, I'm not trying to bum you out, or bash you. You are a beginner, so start off on some beginner projects. Something that won't kill you and/or others if it fails. Quite honestly I don't trust the professors opinion either. I'm going to have to assume he doesn't really know what these are for, and the forces thrust upon them while driving.
To make these work from here (which I do not recommend) you need to:
1)Grind down your welds (like all the way off), remove the paint around the area, and re-weld them. See if you can use the MIG at school with inert gas.
2)Add 1/8" plate to both sides of the arm from the ball-joint to the mounting points. Fully weld the seams in 1-2" increments, moving from place to place so you don't over heat the arm and warp it.
3)Add another (min) 1/8" plate to the bottom, also full width. Weld in the same process as step 2.
At that point the arms should be strong enough that I would trust my life and the lives of others. Again, I recommend you TIG, but at least MIG them with solid core wire and the proper inert gas.
If you really think about it, would you rather over build the shit out of them and never worry about? OR would you rather worry about your life every time you drive and hit a bump?