Good job! Here are a few corrections: 1) you need the word "it" before the verb start: IT started to rain. If you don't use "it", the verb doesn't have any subject. 2) The word "after" is not adequately used in this sentence. It is a preposition, so you would have to say "after SOMETHING", for example "after lunch", "after the sunset", "after 3 o'clock", etc. The meaning of your sentence would be clearer if you used "later" instead of "after".

Today has been overcast.