I am 19 now. I was about your size, maybe smaller, and just slightly stronger at your age. I am now 250lbs, and should squat over 800 next competition easily.
You can easily get really strong over the next few years but just be patient with it.
As far as the diet. Eat more at breakfast. I am assuming the 3 eggs and 2 servings of oats is breakfast.See if you can choke down 5 eggs in the morning.
If you can try and get a shake, or a protein bar in between classes mid morning.
Then lunch, make sure you are eating at least 4-6oz of chicken, and add in some good carbs. Maybe a slice of whole grain bread with peanut butter after the chicken/broc.
Make sure there are EFAs and good carbs in your protein shake. If not, the cheapest way to add it is to just throw in some uncooked oats, and a some olive oil.
The post workout shake needs to have lots of sugar. Try adding 4 servings of nesquick to that... that is an easy way to get the sugar.
Don't bother waking up to eat, that disturbs your sleep cycle. Just drink some milk and eat a peanut butter sandwich before bed.
You also did not mention a preworkout meal. I like something about 45minutes to an hour before. Peanut butter and honey sandwich with some milk was always something I liked.
Doesn't matter as long as you get some complex carbs, sugar, healthy fat, and protein in.
Also if you want to then you could get some BCAAs and take 10g during your workout mixed with 2-3 servings of dextrose based gatorade. I think it is all dextrose based now, I think they got rid of the fructose based.
As far as training, when I was about that size, I got the best results with westside for skinny bastards 3.. you can google it and download the pdf for free.
5/3/1 is ok, but I think the main reason people get good gains on it is just that they are actually following a program where everything is laid out, so they aren't constantly doing retarded stuff. Really it is not optimal. I favor the westide, and subsequent variations.
The Texas Method has worked well with people I have known too, but for everyone I help, at your level, I have them do westside for skinny bastards 3, I make a few tweaks based on their weaknesses, and flaws in the program, and they always get great results.
Your training right now is not optimal at all.
PM me if you want help tweaking westside for skinny bastards, or cannot find the link