Lyme tests are most reliable after 30 days, it takes a while for the antibodies to build up in the system and to be detectable.
https://www.cdc.gov/lyme/index.html
Typical symptoms include fever, headache, fatigue, and a characteristic skin rash called erythema migrans.
No mention of pus filled anything associated with Lyme.
I found a tick on me and called my Doctor. She said to come in immediately if I had any flu like symptoms but made an appointment for a few weeks later. When I saw her, she asked if I had any flu like symptoms since finding the tick (no) and then said we could do the lyme test then (2 weeks after finding the tick) or wait for 30 days when the test was more reliable. She offered the meds for lyme right away but said that if there had been no flu like symptoms or rash that I was probably fine. I choose not to take the meds or get the test.
My husband went in with the rash and was given the initial meds and took the blood test at 30 days. No Lyme found.
Per the CDC website
Ticks can attach to any part of the human body but are often found in hard-to-see areas such as the groin, armpits, and scalp. In most cases, the tick must be attached for 36 to 48 hours or more before the Lyme disease bacterium can be transmitted.
Lyme is scary, I get it. The CDC website has a lot of good info. We try and do a tick check every night before bed, not just a visual check but a physical check. Run your hand over your child, especially if you see a new freckle or a different birth mark. The ticks that carry lyme are small and can look like a freckle. I saw a freckly around my sons groin when he was a toddler. I checked more closely and it was a tick. Make sure to look around where socks and undies lay, ticks hide there.
If you are checking regularly, it is less likely that a tick will be connected for 36-48 hours.