Skip the boot camps and keep your ME job while self learning along the following path.
Picking up the skills you need is a long process, I don't think you can pick it up in a camp, plus it would be tough to go through a boot camp and land an entry level job and have all the knowledge you need.
I would recommend learning HTML and CSS first. (Use MAMP or WAMP and sublime text for your workflow)
The Head First Books on HTML/CSS and PHP MySQL are good starting points.
teamtreehouse.com is also a great place for self learning.
Buy some domains and setup a few websites. You can just use hostgator for hosting, learn about name servers, DNS, FTP, etc.
Then learn PHP and MySQL. (Head First book)
Your engineering degree will be valuable, you could also think about taking some CS courses or do some self study to pick up some CS knowledge.
Once you have experience with basic web applications in vanilla PHP and MySQL give Rails or Laravel a try.
It's tough to jump to a framework without learning to do some basic web applications in PHP/MySQL so you have a better idea of some of the magic a framework takes care of for you.
Check out laracasts.com and railscasts.com
Setup a server from scratch on digital ocean, just so you have that experience.
If you use Laravel there is a great deployment tool, Laravel forge, that configures the server and deploys your app for Rails you can use Heroku for easy hosting.
There are Laravel jobs out there, but Rails jobs are more plentiful and probably have a higher salary ceiling. See what you like and what you enjoy using.
Once you are using Laravel or Rails get some experience with React, Vuejs or angular2.
Once you have the basics you could look at a bootcamp that has a high success rate at landing graduates jobs.
As you're learning setup your own websites, then when you get in to PHP MySQL setup some of your own web apps.
You'll learn most when you're trying to do something on your own. Creating an app that tracks something you collect, tracking your budget, a messaging app for you and your friends, or a private facebook for you and your family.
when you're learning look for stackoverflow in your search results if you haven't discovered it already.
Setup a github account, you don't need to use it initially, but you'll want to build your account to include your best work along with a portfolio.
bitbucket is nice for free private repos.
Use http://getbootstrap.com/ for your own projects.
Once you learn the basics you could build websites for local businesses on nights and weekends, and build up clients/more and more complex projects/clients. Avoid the online freelancing sites where you're competing against the lowest price.
You should also check out
and see if building your own company would be for you.
Also I wouldn't go to the valley unless you get a job there and they assist you with relocation expenses.
Good luck with your transition, remember it's a process so set goals incrementally and keep at it.