They both sound fine. "I don't have so much time" typically appears at the beginning of a longer sentence: "I don't have so much time today to waste on _____ ," but it still works as is. But like Philip said, it can also be used as a comparison, in which case it would be like: "Non ho cosi tanti soldi come pensi." In general though, it's best to stick with "I don't have very much," as it simply sounds more natural in most settings

"I don't have SO much time." = We would understand this, but it sounds a little strange to our ears. This is a difficult question, because there are times when both words are acceptable. For example: "I like this pasta very much!" and "I like this pasta so much!" These mean the same thing and we use them both. (And we would usually pronounce it like "I like this pasta sooooooo much! Hahaha) Philip's answer is correct. "So much" is usually part of a comparison statement. For example, "There was so much work to be done that I didn't know where to begin." In this example, the word "very" would not be correct. Also, I will add that we often just say: "I don't have much time." This expresses the same idea, with fewer words. You can say it both ways and it means the same thing, for example: "I don't have much money." "I don't have **very** much money." "I don't have much interest in that topic." "I don't have very much interest in that topic." Also, with some nouns we would use "many." "I don't have many friends." "I don't have **very** many friends." "I don't have many books." "I don't have **very** many books." "I don't have many stories to tell." "I don't have **very** many stories to tell." Good luck!

"so much" is a comparison. Example: He has more time available than I do. I don't have so much time as he does. So in your sentence, you failed to compare to something else.