Every concussion leaves permanent damage. The big question is whether it interrupts a normal life. For most, they only see a return of symptoms when they are under stress. The repeated question of "what will my future be?" without focusing on the here and now to move forward is counter productive.

Second Impact Syndrome is not from a basketball to the head after 5 weeks.

You still have not explained the first concussion.

What is cognitive regression?

You may have a bit of a relapse from the original concussion. That is not uncommon. It can be from the actual physical impact or it can be from a "Oh no. I took a hit to the head." anxiety. The symptoms are usually the same.

There are plenty of symptoms that will interrupt complex cognitive processes without being brain damage to cognitive processing. Many will find they have a different and less effective way they process ambient stimuli so they have a lesser level of focus on a task so the math processing that was so easy before now takes an effort to disregard the ambient stimuli so it does not interrupt the math processing. Anxiety makes this even worse. A common term for this is "Stop to Think." Often, once the 'Stop other distractions' is done, the thinking is much easier. Doing math with ear buds blasting can become a problem that did not exist prior.

An important concept to understand is: Every concussion is different. What one person experiences has no relation to what others experience. The experts cannot even predict the severity of symptoms. The only predictor is pre-existing conditions. It the person has an intense lifestyle or stressful or anxiety filled lifestyle, they will have more symptoms and they will last longer, statistically. There are always the rule breakers. As I said, there are no normals.

Ok let me slow down and answer. My first concussion occurred when I was at the batting cage and the ball went through the net and hit the side of my head resulting in a mild concussion. My symptoms were brain fog, light sensitivity and cognitive trouble. After 5 weeks I felt mostly healed, until I went to the gym to play pickup basketball 2 days later(bad idea). Someone tried to do the move where you fake pass the ball at someone's head but the ball slipped and hit my head. This caused a spike in my anxiety, but I felt fine after the hit and continued to play. A similar hit with a basketball happened again 2 days later which again spiked my anxiety and caused symptoms to come back. Symptoms include brain fog, light sensitivity, and sensitivity to screens. Seeing as sometimes basketballs can be fairly hard, I'm wondering if I screwed myself over by taking these hits while I was still recovering? With proper rest starting today should I be able to get at least to 95% as this was my first and hopefully last concussion.

How long ago was the original hit? 2 months or so?
Most likely you are much too early to worry about long term issues..
I'd say slow down on activities for awhile, slowly add them back as tolerated, avoid worrying as that doesn't help anything & don't put yourself in a situation where you might get more hits/knocks..

Side of head baseball hit may have misaligned your c1 c2..
any idea on how fast the ball was moving?
softball, hard ball - lobbed or fast pitch
ball sent by a person or machine?

Nothing says you are not at already at 95% but held back by some anxiety. We see it all the time. Resolve the anxiety and the recovery is obvious. Give yourself a break.

If you stop over analyzing the situation and yourself, you will do much better. There are no answers to your questions. The best you can do is take care of yourself. No contact sports. No batting cage without a helmet. Read the Vitamins sticky and get started feeding your brain. Learn about how you can reduce your anxiety.

I looked up the speed of a pass and the weight of a basketball. At most, those hits were at a subconcussive level, no more, but I doubt it.

When you think you are cognitively struggling, stop and observe your environment. The sounds, sights, and even smells and other sensations that can over-stimulate you can make it difficult to process the cognitive task. Try reducing those stimulations and you should do better. Your anxiety makes those stimulations even more difficult to block out.

Often, recovery is a process in learning to relax and focus. Give it time.

My best to you.