Yesterday after dinner, I went out for a stroll (is there any difference if I say 'a walk'?) with my dog. I unlocked dog’s chain (I'd prefer, 'removed the leash' or even better 'unleashed him') so he can could roam freely (can I say, run around) and I was standing next to my car parked under a tree (personal preference 'standing under a tree next to my car'). I heard a voice as if something is cracking (I suggest 'heard a cracking sound' - your phrase sounds like it turned out it wasn't a crack but it was), very thin sound as if it is coming came from very far away place (doesn't sound natrual to me, maybe 'afar'). But then after a few seconds (I'd prefer 'A few seconds later') a huge branch of the tree (personal preference, 'a huge tree bracnh') fell just next to me. (F)or a moment I didn’t realised what happened. But after coming to senses lots of horrifying images conjured up in my mind and it made me very afraid. (I)f I had have been standing even an inch ahead that branch would have fell fallen on my head and it would have hit me badly and injured me severely. I am really thankful to God that he saved me or else I would have been in (the) hospital or may be strolling( I'm not sure on this, in writing, I guess I would say 'in heaven strolling') in the heaven ( or hell :p)!
(As you can see, I have so many questions myself. I don't think I've helped you in any way. Just make sure your tenses are consistent, at least in writing. I think your tense switching is acceptable in speech. After all, native speakers do that all the time but in a combination that remains mistery to me. Maybe a native speaker can comment on that.)