I checked the 1860 census and could find only one Miles Costello, he was born in PA and was less than 1 year old in 1860 so I think we can count him out!

The only Costello in the 4th Tenn. was Martin Costello/Costillo who enlisted in 1861 and was still shown on an 1864 muster roll. If this is your man you can get his full service record from the link at the top of each page on this site.

Unfortunately Costelow is one of those names that can be spelt in a myriad of ways, I've noted Costello, Costelo, Costillo, Costilo, Costellow, Costelow and there are probably others, so you will need to check all possible permutations.

Alan Thrower
England