I am not sure if this is usually happens here so I need some advice.

I bought my dream blouse and belt at New Look yesterday. After I paid it and was about to leave the shop, the security alarm at door ways alarmed with people watching. I let the cashier check it again and they said sorry as they haven't taken the security tag properly in my blouse. But it happened again when I was about to leave the shop and let them double check again. They said never mind I can leave the shop but I insist them to check it and thinking it might be the belt security tag. Then they removed the tag and say sorry again.

This felt me embarrasing as people in the shop no doubt thinking I'm a thief and I don't like them for being incompetent.

I am planning to make an official complaint with this shop.

Is that a good move?