So it’s possible that it’s not tick since other insects make a bullseye rash. Is the bite decaying? Warm to the touch? Do you have a fever or other symptoms? Could indicate something else. I recommend getting on doxycycline ASAP. Ticks also don’t always attach, they can bite and move on if it’s unfavorable it’s just not common. I’m in the same boat and have been on doxycycline for the last week to cover any bases.
that’s definitely not the standard. tick bites are extremely common at my workplace (literal national park service) and they don’t recommend going to a doctor unless you have symptoms. only about 20% of ticks even carry lyme, and if a tick is attached less than 8 hours and properly removed your chances of lyme even from an infected tick are almost 0. i understand wanting to treat just to be safe but if a tick is attached less than 8 hours it’s not appropriate to take antibiotics.