Let me add on to this from personal experience when I started graduate school to become an experimentalist. My advisors were really big on being able to build and/or fix equipment in the machine shop, since the shop people were not around on weekends and holidays when were often using the beamline. So, first they wanted me to draw something up and send it to the shop to be made. I took my autocaded drawings and turned them over to the shop and when I later came back and asked about the drawings, the head of the shop said, '"Oh, you mean your cartoons?" So, the next time, I talked to people who knew more about how to properly draw and dimension something so that I knew more about what to use for references to ensure the critical dimensions were well defined without specifying everything so tightly that as the said to a colleage, who specified everything to a thousandth of an inch, "Well, we could use a hammer to pound it together."
Next lesson was using a milling machine. The shop supervisor walked me over to a milling machine, put my chunck of metal in a vise, showed me how to put the endmill in and snug it up, turned the machine on and the walked away and said good luck. Fortunately, I am fairly mechanically adept and not afraid to bother people, ask questions and let them make fun of me, so that all worked out and I not only got my pieces machined, but learned even more about how to design something in a way that lent itself to being made as easily as possible. After this I went through a similar process leaning to use a lathe and grind my own lathe tools, which furthered even more my ability to design thing with a conscious effort to do so with a picture of how someone would have to actually use my drawings to make the pieces.
Next was my attempt to learn to silver solder fittings to a one of a kind magnet that had burned up and I had to rewind with copper tubing. As luck would have it, I immediately used the torch to melt two fittings tht I thought would be nearly irreplaceable. After a half a day of having the machinist make fun of me and tell me that had no ide what they were going to do now, they finally just laughed and made a couple of new fittings for me By the time I finished grad school, I was made an honorary machinist and give my own tools.
Let me add that I never took an autocad class, or a class in mechanical drawing and was just lucky that I had spent some time whrn I was younger working on cars, so that I wasn't totally mechanically declined. In the end, the experience of doing these things myself was one of the most valuable things I ever learned and I have been able to make my own experimental apparatus where the cost of buying things and trying to assemble something close to what I wanted was so cost prohibitive that I could never have been able to do it.
I've managed to even design some things that were inherently, but unavoidably dangerous where the lab director overruled the saftey engineer as being excessively paranoid.
If you can find a maker space with some machine tools, and you do everything yourself, your experience making and building your own designs will teach you a great deal about how to design for manufacture by real people using real machine tools. That will lead to getting the things you design finished much faster, easier to service and more likely to be what you really want and work the way you expect. There are many things I could never have done without being able to do them myself simply because of price, the time lag in finding a shop to make the parts and trying to explain to a shop why some things had to be done a ertain way.
Sorry for the lengthy story here, but, back when I was in grad school, getting advice on how best to do things from newly minted MEs or MEs with just a few years experience was more of a hinderence than anything else. They were good a drawing things, telling me to scour the ASME manuals, and the like, but their actual experience translating what they were designing into things that were supposed be used in the lab, often resulted in some quirky designs that were difficult to fabricate and not always as easy to use when attaching them to existing equipment. (Or as the shop guys referred to things, "An engineer's wet dream.")
There really is no better way to integrate everything you've learned and become creative than to get some hands on experience with every step from design to finished assembly. And, I would like to especially emphasize the creative aspect here, because there are many ways to design the same widget, but a great deal of creativity might be required to do so in way that makes it easy to manufacture consistently, inexpensively and service later on. I've seen one person design something such that once assembled, none of the bolts were accessible to disassemble it later. You don't want to live something like that down. :)
As an ME, you have a lot of opportunity to be creative and demonstrate your creativity by thinking through the entire process and not just doing the most obvious, clumsy thing that initially comes to mind, espeially if you choose a career as part of scientific group that needs many one of a kind pieces of apparatus designed and built. There , you have the chance to be an artist.