Is this sentence grammatically correct?
There's nothing wrong with the sentence.
There are some people who would tell you to remove the comma before "and" but I am not one of them. Keep the comma.
If your list included phrases that required commas, the commas to separate the items would be semi-colons:
What may sound strange is the odd passivitiy to "my leg was broken". I would usually say "I broke my leg" and not worry about forcing the items in the list to be parallel.