As far as Makefile dependencies my advice would be to not worry so much about it. It can greatly optimize build times after the first build so it's definitely useful, but as you realize it's a lot of work to maintain and keep up to date. It's really the job of an automated process, but that basically requires the Makefile to be generated instead of hand-written. For the purposes of just getting the game built you should suffice with a much more simple file. If it takes more than 5 seconds to build then you can try to optimize your process for you. For users that build once and play it though even 30 seconds or a minute is acceptable. Insert: Welp, I guess it is useful to define all headers as dependencies so objects are rebuilt when you change a header. So I guess you're right and I'm wrong. The poor man's solution could be to delete all objects before building them.
Allegro should be installed in the system include directories. When you specify -I/path/to/allegro you're defining that as a system directory. The #include "" syntax would search relative to the current file also, plus "quote directories". This is the first I recall reading about quote directories, but apparently you can add paths with --iquote (I've never seen that before either). Quoted paths are meant for headers in your program. Third party libraries, whether part of the OS, toolchain, or otherwise are all considered system headers.
First verify where Allegro really is. /c/CodeBlocks/allegro5 seems odd to me. Maybe /c/CodeBlocks/include/allegro5 makes sense. Windows' cmd or Unix's ls and find are your friends.
Here's one that appears to work in Debian, but I haven't tried actually running the game yet.
1ALLEGRO_MODULES = allegro-5 allegro_audio-5 allegro_acodec-5 allegro_dialog-5 allegro_font-5 allegro_image-5 allegro_primitives-5
2CFLAGS = $$(pkg-config --cflags $(ALLEGRO_MODULES)) -Wall
3LIBS = -lm $$(pkg-config --libs $(ALLEGRO_MODULES))
4HEADERS = $(shell find src/ -name '*.h')
5OBJECTS = $(shell find src/ -name '*.c' | sed -e 's/\.c$$/.o/g')
7.PHONY: all clean
12 rm -f lc src/*.o
15 gcc $(CFLAGS) -o $@ $? $(LIBS)
17%.o: %.c $(HEADERS)
18 gcc $(CFLAGS) -c -o $@ $<