I am Eric Johnson. I'm going to qualify my answer as being a instructor at a bootcamp in orange county CA but also as a person that learned all of his programming skills with no formal training.
If you are trying to learn all of these skills in 3 months you should consider some type of structured training program. I am not saying a bootcamp is the correct answer for everyone, even though this is highly recommended and http://www.LearningFuze.com has a program tailored to your specific needs :)
... sorry back to my point. If you attempt to learn from books and random online courses here and there you will have huge holes in your practical knowledge. Not only will your knowledge be limited, it will likely take more than 3 months of work even at 8 hours a day.
Structure is important
A structured training program will give you a good path to follow (The internet is littered with forks in the road), practical experience, and mentors to let you know when you have gone down a hole that you may never be able to dig yourself out of. Even if you never consider a bootcamp I would make sure you talk with an experienced developer who is willing to mentor you through this process (open source developers are really open to this).
With all that said, I would start down this path if you are choosing to go at it alone:
Read HTML tutorial and try all examples HTML Tutorial (60 ish tutorials)
Read CSS Tutorial (Another 60+ tutorials)
Read JavaScript Tutorial (Another 60+ tutorials)
Read SQL Tutorial
Go through these coding practice tutorials HTML/CSS - Code School, JavaScript - Code School (29$ a month)
Practical experience
Once you are done with all of that, probably 3-4 weeks worth of work. I would think of something you love doing / are passionate about and how could a web application make that activity easier / more efficient. The reason I suggest this is because it won't be easy and learning through a passion is how I got through late nights and difficult concepts. If you can't think of a passion then recreate an already existing application, this may not be as rewarding but you don't have to figure out the functionality because it already exists.
Hope thats helpful,
PS. You can continue with JS on the backend by using NodeJS don't worry about learning another backend language for the time being. Learning any backend languages will be a difficult transition because the concepts on the backend are not visual and therefore not easy to see the console.error of your ways.
Mr. Quincy Larson suggests:
SQL
The best way to learn SQL and relational databases is to take Stanford's Database class. This course is self-paced and free. After each set of video lectures, there are (surprisingly challenging) SQL challenges.
HTML5 and JavaScript
The following will take you about 600 hours. These are all free, self-paced, and browser based (No need to configure a dev environment).
Basic HTML5 and CSS
Responsive Design with Bootstrap
jQuery, Ajax and JSON APIs
Basic JavaScript
Basic Algorithm Scripting (in JavaScript)
Object Oriented JavaScript
Intermediate Algorithm Scripting (in JavaScript)
Functional Programming (in JavaScript)
Advanced Algorithm Scripting (in JavaScript)
Front End Development Projects (building single page apps on CodePen)
You'll also earn a verified Front End Development Certification in the process.
Learn to code
You can be job-ready with these skills within your 3 month horizon by using these resources.
Stefan Ritter, Lead Front-end Developer suggests :
The single best resource to learn SQL is through Stanford online's Intro to Databases course - it's epic:.
Stanford Online: Introduction to Databases
Coursera: https://www.coursera.org/course/db
For HTML I would just do Codecademy, there really isn't much to learn here. Also don't forget to learn CSS while you're there...
For JS and Frontend developement, the best book to start is the free Eloquent JavaScript.
Once you're done with that, or at least have the basics down - I wrote a blogpost on how I would learn JS if I were to start over now