Compelled to say the term ‘words’ when I stutter. Help?

Compelled to say the term ‘words’ when I stutter. Help? So I’ve always had mild cluttered speech and stuttering that comes and goes. It’s minimal now but was extremely bad a couple months ago. Long story short when I got frustrated from not being able to say what I wanted to, I started expressing that by interrupting my sentence with saying the term “words” in exasperation. Example: “Hi there! May I have a- have a- have a- have a- ‘words.’ May I have a peppermint frappe?” This usually worked cause it would make whoever I was talking to laugh and usually they understood I was stuttering without me needing to explain it. They would chuckle and say “I know how that feels” which helped alleviate the social anxiety of the situation. I used to consciously say it to purposefully give myself a clean break to start my sentence over. However as of late I noticed that when I do stutter even on occasion it has become more compulsive… almost like my stutter has absorbed it. Example: “Hello. May I have a- ‘words’ have a- ‘words’ ‘words’ have a- ‘words’ have a peppermint frappe?” While this doesn’t happen as much, it often feels embarrassing when I subconsciously insert the term ‘words’ now as part of the repetition rather than a conscientious effort to stop it. I don’t know if this is classified as a nervous tic or just my brain associating the term ‘words’ with my stutter now so I feel compelled to say it with the stutter or what. Anyone else does something similar? Any tips to stop it?