arms waving

Hi,

She was waving her arms as she walked.

Do you mean as if she was angry, or perhaps as if she was trying to say 'hello' to someone far away?

Clive

When you run, your arms swing alongside you. I'm not talking about wave
She was swinging her arms alongside her while she walked.
Her arms swung alongside her as she walked.

Hi,

Hmm, you posted about waving but you are not talking about waving.

Clive

I thought waving made sense, turns out it doesn't mean what I looking for. What way would you say?

I don't know if there is one single word that would describe the synchronized movement of arms and legs as a person walks or runs.
I can understand how "waving" would come to mind, but it is not the word you are looking for. I would just describe the fact that as the person ran, their movements were synchronized.

What about

Her ams swung alongside her as she walked.

is "alongside her" grammarly correct?

Yes, that's correct and meets the description. Good work!