What you are looking for is a mixer, like the Black Magic ATEM. This type of gear is expensive though and usually only used by TV-studios and professional broadcasting services, so I would think twice before buying one.
An alternative is hard to come by, since you need HMDI or (preferably) SDI inputs that get mixed, which you cannot simply do on a PC or Mac.
A quick google search gave me dozens of options. You can use yellowduck for example. Here's a tutorial on how to use it. An alternative is promovgram. There really are a lot of options, so I would recommend just googling yourself.