I think there may be a bit of overmedicating going on here. Pin holes
in the tail are nothing to worry about and will heal themselves in a
couple of days. Even more serious fin rot can often be treated
successfully by increasing your water changes and monitoring your water
parameters. To put an already stressed fish through a course of
antibiotics may add additional stress.

That said, it's important to finish the course of Ich treatment. As you
may or may not know there are three life stages to these parasites and
they are only affected by the medication a couple of days out of the
cycle so if you stop treating the Ich it's very possible you will miss
those days and they will return in greater numbers.

Whether or not you finish the treatment of antibiotics is sort of up to
you. Antibiotics should be followed through because under-medicating or
shortening the course may lead to antibiotic-resistant bacteria. On the
other hand, unnecessary treatment may be harmful to your betta.