Gaining 15-20lbs in two months is a very lofty goal. I don't know what the standards are for beginners gaining weight, but I'm pretty certain that 10lbs a month is a lot if it's not mostly fat.
The best thing I can say about your workouts is that they include lots of full-body lifts. It's generally a struggle to get trainees your age away from doing 15 sets of curls, so a big congrats on that. You may want to consider the possibility of being able to improve on your form some. I "squatted" for a good year or so without really getting it right until I worked with a trainer that actually knew how to squat. Quite simply, there's a heck of a difference between a poorly-executed and a well-executed squat. It may be worth your time and money to find a good trainer, if only to help you for a few months.
Now as for negatives, six full body training days seems like a hell of a lot for a beginner. You're probably more knowledgeable than the average gym-goer, and with that extra knowledge, you probably feel like you want to do more and more. In your case, less is more. Unless you're on drugs and eating a truckload of food every day, you're almost certainly not ever fully recovering.
I know that it can suck to think that you're doing too much and you have to deviate from your original plan to do less. I've been there, but when I finally stopped trying to train twice a day, five days a week, I actually started to get stronger, feel better, and turn my body composition in the direction I wanted.
Think about that. Do you frequently feel tired? Do you have trouble making yourself want to go to the gym? Are your joints always achey? It might be time for a deload and to do a less so you can grow more.