I wouldn't say it's a bad headache. On a 1-10 it's a 3 at most.
I don't have it when I first wake up, but after 20 minutes or so it comes on and lasts all day.
I tend to have headaches quite often and that sounds similar to the sort I have - they got a bit worse for a while after I had the vaccine, but I never thought about seeing anyone about it, it doesn't sound like yours are anything to be concerned about either.