I agree. i also think you need to do a bit of homework on the background of ID and what the basics are. Basic traditional ID is NPD. Yes there are many different avenues that ID has gone down in the recent years (UX, Service Design, Design Thinking, etc…) but for you I feel NPD should be your focus.
The skills are an issue. Rough sketches of a floor plan is much different than detailed usability and sketching out a form exploratory. Stick with the skills you are good at. I am reading things around understanding of physics and mechanics. That is great! Where you are lacking in traditional design skills, a designer maybe lacking in your strengths. That is what makes a successful team. Trying to be something your not is only going to cause you frustration. Embrace your skills, master them and push them to new opportunities. When doing your homework, start to understand Engineerings role in NPD. Then evaluate your skills and look at where you are strong and where you may need to grow. You can then research design firms or corporate in-house design teams and start to understand how you may be a fit.
I would also encourage you to start networking. Reach out to either firms in your area, designers in the area, people you may find online, or whomever may interest you and start getting to know the community. Look into your local design organizations. If you are in the states, check out IDSA. Start conversations and ask all the questions that may be a bit fuzzy to you. Designers are always open to having a beer and chatting. It helps when you are buying. 
That being said, make sure you are doing your homework and are educated with what you are looking for and how you want to get there.
Remember career changes take time especially when you are trying to do something totally new. The more prepared, and connected you are the happier you will be with your move.
J