Your coin is not streaky. You are.

A fair coin has no memory, and a specific run is just a specific pattern. Six heads in a row is one pattern out of every possible six-flip pattern:

Unlikely in any given six flips — but flip 200 times and there are 195 overlapping windows of six, so expect roughly three such runs. Streaks are not rare; they are scheduled. And after five heads, the sixth flip is still exactly 50/50.