What do you think will happen if you use the toothbrush without sterilising it? What are your feelings about the thought of using an unsterilised new toothbrush? Do you feel dread or unease or something else? Would you be able to use it after being re-assured it is clean/not handled by anyone else/packed in a clean way or would you be unable to cope with that?
It may be you have low grade OCD - just about everyone has OCD behaviours to one degree or another after all almost everyone has Intrusive Thoughts (the kind of thought that says 'What if I kissed my boss right now' or 'I might shout Piss off in the supermarket queue') or the urge to (re-)check the cooker/iron/front door just to make sure you turned it off/locked it or the urge to do a ritual to make something/someone safe.
How you deal with those thoughts/urges depends on whether you have OCD or not - if you ruminate on why you thought about shouting in the supermarket (did you want to upset the old lady standing next to you, are you a bad person for thinking about shouting bad words, what else are you capable of doing in public....) or doing something to mitigate/atone for that thought (performing a ritual or behaviour that comforts or reassures you) then OCD is likely. If you shrug it off and think 'that was a silly thought of course I'd never do that!'
In doing what you are doing - having a thought that 'they' might have done something to your toothbrush which is outside your control which means you need to perform a ritual to comfort and reassure yourself (i.e. boil your toothbrush), this thought is unreasonable (i.e. the majority of people on this thread wouldn't think that about the situation/item/thought) then it the action/behaviour you do following that thought is also unreasonable. Sorry!
I say this as someone who has OCD and who has these same kind of thoughts/behaviours (e.g. having to repeatedly check on the children in the pushchair if they were facing forwards instead of facing me as they may get stolen or die without me noticing or being aware - while I was still pushing the pushchair even on an empty path
).
If this is your only 'quirk' then it's probably okay(-ish) to keep doing this, however if you do other things (or start to do other things) to cope with things outside your control it may be wise to see your GP for a referral to CBT therapy or something similar.
I do hope you don't take offence at this.