@Heather-Boyd There's alternatives to illustrator, Inkscape one of them, just google it. But you just going to end with another program that you have to learn to use it. If you have illustrator, I'll recommend to sit through some youtube tutorials and learn to use it. It is worth it!
Unless you want to use Photoshop, the vector tools in photoshop are real good today and if you only want to create a logo don't need to learn a new program.
Have a nice day!