When you take antibiotics does your immune system not produce those memory t cells to combat that specific bacteria in the future? or does the antibiotic kill it to too fast/or does not recognize it for not "battling" it by itself?

Far too complex to fully explain here. You can learn more at Mayo Clinic or Cleveland Clinic sites. In brief: antibiotics do not impede the immune system's response to any infections, but provides supportive effects by suppressing or killing susceptible bacteria. This enhances efficiency and successful outcomes.

Agree with Dr. Mechanic. Most antibiotic do not suppress immune response. Antibiotics are essential for bacterial susceptible to the medication. For healthy diet: http://www.choosemyplate.gov/., exercise 30 minutes/day, drink enough water daily so your urine is mostly colorless, have safe sex, no tobacco alcohol weed or street drugs. Get HPV and Covid vaccines. Wish you good health!