Just curious to know, how could a Mechanical/Industrial Engineering degree, and an IT degree (one of them) lead to a job in the computer software industry?

It's certainly understandable that you might be anxious about receiving criticism, especially if you are an innovator. It's easy to say, "just ignore them when you know you're right.", but the reality is we are all sensitive to critiques. One must grow a thicker skin with each turn of the Earth around the sun. As we get older and become more a part of the DOING society, our risk of being put down increases. Each of us must develop mental toughness through meditation, just plain self-talk, writing in a journal and basically doing what you think is the right thing all the time.

Be sure you document EVERYTHING you do on the job in your own personal file. Be sure to include comments and input from others in your sphere. Periodically review that daily journal and look for patterns or high/low points that can be addressed. We all are, after all, on our own.

I hope that helped.

Synergies is the word. What are the synergies between software engineering and mechanical engineering?

Plenty. General Electric makes huge machines like locomotives and turbines. They just opened a software center someplace in the California Bay Area to figure out how to use software to make those machines work better.

Airplanes, helicopters. Airbus makes fly-by-wire control systems for their airliners. It's actually fly-by-software.

Watch car commercials. Do you see those demos of self-parking cars? That comes from a merger of software and mechanical engineering. Carry that a little further to Tesla's driver-assistance feature set and to self-driving cars, and you see a future in that field spanning at least half a century. And software-driven engine controllers are in pretty much every jalopy made after about 1992. Look at the Volkswagen diesel-engine controller scandal for example.

Heating and air conditioning, especially the control systems, are made from mechanical + software engineering.

Robotics.

You can do this yourself. Get a Raspberry pi and a robot kit, and mess around!

Don't be afraid to incorporate all those fields of interest to some degree, because in today's manufacturing and design of computers, they are all very much integrated. You will not only be dealing with software, but firmware and hardware too, especially when it comes to designing and building a complete system.

If you are an innovator by nature, be advised that not everyone you will meet will appreciate your bright ideas. There is still much "not invented here" mentality as well as egoists who can't stand to have their work examined for improvements. Tread carefully, but don't keep your light under a bushel.

Good luck.