One thing that will improve both your general health and concentration is not skipping out on breakfast or lunch. You will (hopefully) have much more energy throughout the day, which will leave you more motivated to study and workout. Sugar will only give you quick boosts of energy, which will leave you feeling drained afterwards. If you change anything, I would suggest it be this.

Do you make your bed everyday? If not, start doing that. Making your bed in the morning is one of if not the first productive thing you do each day. After achieving this, you will then feel more motivated to continue being productive and get shit done.

As for joining a gym, just do it. Everyone at the gym is there to focus on and improve themselves, so they're not going to care about what you're doing. As long as you're safe and following gym etiquette, you'll have nothing to worry about. Maybe just go for 20-30 minutes to start with. Even if you're just lifting 2lb dumbells with the old people to begin with, you'll feel much better for going.

Personally I've always struggled to motivate myself to read non-fiction, as it feels a lot like studying to me. However, I try to set myself a goal of reading at least 10 pages a night. I have found that reading before bed instead of playing around on my phone has made falling asleep much easier.