Reddit reviews Evolutionary Genetics

You can learn genetics without having to undertake any wet laboratory experiments in molecular biology/genetics.

Some suggested reading...

• Human Molecular Genetics : Great overview of the genetics of human diseases.
  
• An Introduction to Population Genetics Theory : very heavy on the mathematics (I spent ages searching for this 1970 out of print book, good to see its now reprinted).
  
• Evolutionary Genetics : excellent book, includes questions/tasks at the end of each chapter.
  
• Recombinant DNA : very good primer for molecular biology.
  
  There is tons out there, if you want to do some "experimenting" you could try writing computer simulations of changes in gene frequency under selection pressure. Learning to code is also an invaluable skill/tool too these days.
  

Evolution occurs over many tens of to hundreds of thousands of years, and even then, at the scale of single proteins such as haemoglobin that you are talking about. The development of an entirely new organ in response to an environmental change occurring over one organism's lifetime is preposterous. Cancerous tumours do not suddenly turn into new organs that can metabolise carbon, go and read a book, specifically, if you are remotely interested: This and this. These are undergraduate level textbooks so even with as basic an understanding as you seem to have, you should be able to pick them up from the start if you stick with it. Your grandma isn't going to grow an extra arm because a new video game controller comes out that has 3 joy sticks and you want to play it, do you understand?