I had one small freelance project last year and it looks like TT requires me to upgrade to more expensive software in order to add expenses for this job. Am I correct?

Freelance work is considered self-employment income.  If you have expenses to report related to that business income, you will have to use TurboTax Self-Employed, if you are using the online version of TurboTax.  If you are using the Desktop software, you can use any version; however, you will only receive the step-by-step interview and help related to self-employment if you use Home & Business.