Scouting: you didn't see the hellion drop coming. Such things like the drop or a banshee can just end the game, try to scout more or anticipate it (timings, see further). He sneaked an expo while you sieged him, just send a marine or scv out to scout for it sooner = at the start of your siege in this case. Also, you sieged him around 13 mins, why not expo immediatly? Nothing on ground could leave his base unnoticed. I think your 3rd started building around 15 mins?
The build: there's nothing wrong with reaper expo and a factory but u went factory and a barracks. Its not really optimal to go stim and starport and techlabbed factory that isn't even used because u made a mine after the tech lab. Standard is 2 barracks after CC for straight bio, and factory - starport that can go mech or bio depending if u want to be aggressive first and so on.
Strategy: To me TvT feels like I need to see what he is doing so I know if I can cut corners: can I build an early 3rd? Can i go double E-bays? Do i have to build a turret? Thats scouting again and having a plan for the game.
( This is my personal take on it)
Vs mech I go full bio to multitask, mass expo, to drop and tear him apart, or I go bio tank and into air when he can't pose a threat and has to defend but I do expand slower, but I will have a better army because i get a terran deathball faster (as long as you don't die to an attack = scouting). = strategy: do I want to play High risk, high reward, or a more safer, slower style that CAN (not in all cases) be more reliable.