I have hashimotos and at times very bad anxiety. is it still advisable to take a methyl pack for non infectious minor tooth pain?

I am assuming: (I hope correctly) you mean a Medrol dosepak, a package of multiple methylprednisolone pills to be taken in tapering doses for numerous conditions requiring (cortico)steroid treatment. Non-infectious minor tooth pain would not be one of them for anybody, whether or not you have thyroiditis or anxiety. Consider alternate medical/dental care if someone prescribed this for this condition. Stay well:)

Dental care: You need to practise better dental hygiene. If your toothache is from teeth-grinding, see a dentist to get you a mouthguard to wear at night. If this is from a chronic sinus issue, need to get the sinusitis treated. Steroid is almost never indicated for toothache due to its side effects.

I'm sorry: Cortisone is not appropriate treatment for toothache. Either you have a fracture, a deep cavity (infection within the tooth), or an abscess (infection spreading to other tissues). In any event, what you need is immediate Dental care. Please don't put it off.