I am asking an expert for a piece of advise, I have wrote the message, but he did not answer. I am going to write a follow up. Which one is more tolerant and correct:
1) Hi Ann! How’s it going? Did you have time to go through my message?
2) Hi Ann! How’s it going? Did you get a chance to look my message?
The second one is missing the word at after look:
Hi Ann! How’s it going? Did you get a chance to look at my message?
Once that is fixed, both choices are OK. The second one is maybe slightly more polite since looking at a message is simple but “going through” sounds like more detailed work. I think you are just trying to ask if she has started considering your message, not whether she has analyzed it in detail.