Making my own programming language
I second the recommendation to invent a grammar and use a real parser.  A recursive descent parser is very easy to write, and a great place to start.  You might also have a look at a PEG (Parsing Expression Grammar).  It's almost as easy to use a PEG as it is to write a recursive descent compiler, and a PEG can parse more grammars than can a recursive descent compiler.
Here are two PEGs for Python (I haven't used either of them, so can't vouch for them):


pyPeg
parsimonious


I don't see a good reason to get the Dragon book yet.  Much of what it teaches is how to write the LEXX/YACC type tools, along with language theory.  I think it's too deep and too low level for someone who just wants to try creating a language in order to see how it's done.  If, however, you do want to dive that deep, it is a very good book.

I would, for now, steer clear of a traditional lex/yacc setup.  That's a harder road that can wait until you've had some experience with simpler schemes.  However, if you do want to go there, PLY is a lex/yacc type parser for Python.