There are many routes that you can go. Before you do anything though you may want to look into the financial viability of your product (manufacturing, marketing, sales, insurance, distribution, demand, how many you need to make per year). When you do this, be sure to include whether you will need a patent (and whether international patents are needed); while you research the patent, you want to decide which type of patent you need; as you do this, you may want to do a patent search. Right now, you may be thinking "why is he talking about this? I just want to get a prototype made".
The reason I discuss financial aspects and marketing is that whoever builds this needs to understand how much it has to cost per unit and number per year made (dictates what manufacturing processes are chosen and therefore dictates the limitations on the design/materials). I have had clients in the past who refused to think this far said "just make a prototype". After we did this and did our engineering, they crunched the numbers and realized that they want to mass produce it in larger numbers or in another instance they wanted to make less at a higher costs which caused us to have to redesign certain components. They understood that it was their fault but it still impacted the financial viability of their company by causing them to spend more money than they had to before making any revenue (imagine a potential investor's reaction when you explain why you explain why you essentially have 2 viable designs for one product).
In any case, I digress. After you do all this and figure it out, you can look at various avenues for design/engineering.
1. Freelance mechanical engineer - usually cheaper however you have to be sure that he has the capabilities / experience to do it all or you may have to dedicate a lot of time to managing the project in addition to figuring out the business/regulatory side of your product. Also, with less cost, you will have more risk that he isn't who he says he is. These days, I have heard of a lot of dishonesty when it came to experience from downloading 3D models, copy+paste pictures, and lying on resumes.In any case, keep us posted or start more threads if you have any other questions.
2. Engineering firm - They tend to be more pricey than the first option but usually have a reputation that can be confirmed. Also, this option may not land you with a firm that has as much experience in what you need done compared to other options. This option also involves less management time and is more secure for your idea than 1. We are an Engineering / product development firm and may be able to help you if you'd like. I'll let you contact us if you are interested.
3. Machine builder / machine building shop - these are possible to find but may take a while to find. In my experience, they seem to be centered on more of the 1-off jobs although you may find a shop that can transition their prototype into production. I honestly don't know too much about this so you will have to do your research in or others may be able to chime in to help with this route.