Sorry, no. If it were proof, it would have very square and sharp rims and a mirror finish in the fields. You have a Philadelphia minted cent.
You're not going to find a No S proof in change. First, think of how uncommon it is to find any Proof only issue in circulation. Yeah, it happens but think of what needs to occur. Somebody has to go through the effort of breaking open the hard plastic holder and then deciding to spend the coins at face value. Does it happen? Yes. Is it a common occurrence? You decide. In 1990, the mint made over 3 million proof sets. How many No S proof pennies were made? It may be 200-500 depending on the source. So, let's say someone was lucky and got one of the 0.01% 1990 proof sets with a No S cent, and they also happened to be in the small minority of non-dealers that decided to break open the set and spend the coin at face value. And, of all the cents out in circulation, you just happened to find it. Can it happen. Yes. What's the probability of it happening? Too much math for me today. If you really want to find a No S proof, you need to search the proof sets. 1990 is a cheap set and there is a chance that some still haven't been checked.