Too late now but for future reference always keep a bottle of rubbing alcohol in your first aid kit precisely for removing ticks. Pour a capful on the tick then take your tweezers, grasp the tick as close to the head as possible (often times it is embedded) then wiggle the tweezers back and forth gently until the tick lets go.
If it still doesn’t let go easily, another capful of alcohol may be needed. It’s usually the newly attached ticks that are the hardest to extract, IME. Those fully engorged (roley poley fat) are easy to remove. Not that most of us haven’t done this but ticks shouldn’t be pulled off with fingers precisely because the heads tend to stay embedded.
Another PSA: Both my vets (equine & small animal) as well as my MDs, have suggested saving the tick in a glass container in case any illness develops down the road. In fact, the first question from everyone of these folks has always been, “Did you save the tick?” Apparently, it’s much easier and more accurate to test the actual tick for the more common tick born diseases than to rely on antibody levels from the bitten individual at a later date.