On move 16 instead of playing Bf5, you needed protect, blockade, or remove the threat of the queen from being able to hit the weak f7 and h5 squares which forced perpetual check. Moves like Qf8+ which protects the f7 square with tempo by giving check, Nf5 which can go to h6 to block the queen from the check when the king goes to H file after Qf7+, Be6 which protects the f7 square, or Nxe5 to remove the ability of white to go to f7 with the queen as she'd no longer have protection would all be candidate moves, the last suggested move being the favored one as your up significant material so trading down more would only increase your advantage.
Threefold-Repetition Draw...?
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Yes, it actually happened, but was there any way I could have gotten out of the trap in which my opponent had me snared?