Hi, thank you for asking. I've not used Grammarly but it looks like they use AI. I would say yes use a dictionary to check spelling of any individual words.
I would also suggest proofreading it - take a break after making it first, so you can come back afresh. Even if you were using AI (not for this jam) you'd still need to proofread it yourself as AI isn't accurate, so this isn't really an extra step. If you're using it for anything professional e.g. selling it or using in a portfolio for job applications, I'd even get someone else to proofread it for you. Maybe someone you know can do it as a favour.