The accounts of Severus Alexander's life are very limited by contemporary ancient historians and their usefulness is widely debated.   I have provided a list of ancient and modern historians who covered Severus Alexander and links to their works where possible.     In regards to modern historians, I have also listed the works I recommend one read.

Primary References (ancient historians)

Cassius Dio Cocceianus (Dio)  - regarded by some as the best primary source on Severus Alexander.   Unfortunately only 1000 words of his work, spanning the first six years of Alexander's rule, survived the ages.  

Herodian - provides an extensive record of the reign but some considered not to be very reliable.  Other consider it to the only complete account.

Marius Maximus - his writing were lost but are later referenced in the work, Historia Augusta (considered by many to be a collection of sensationalized scandal mongering). The section "The Life of Severus Alexander" was supposedly written by Lampridius.   The entire work's authenticity has been debated for some time.  It is now believed by many that the entire work was written or rewritten by one author around the year 395 AD. 

Modern References I recommend

There are a wide variety of modern historians who've written books concerned with either some or all the emperors.    I've found it difficult to find a decent handling of Severus Alexander.      Here's what I recommend:

Severus Alexander and the Severan Women by Robert L. Cleve, PhD, is the most comprehensive work I've read on Severus Alexander and the women who guided his life.   This is Professor Cleve's doctorial dissertation and can be found on various sites that you purchase dissertations.   Highly recommended for anyone who really wants to better understand Severus Alexander better. 

The Decadent Emperors also under the title The Young Emperors by George C. Brauer, Jr. is a super book covering more than just Severus Alexander.    The chapters devoted to Severus Alexander read very well and provide a good amount of detail.   Highly recommend.

The Severans by Michael Grant is another great book by a well know historian that covers the Severans quite well.   It unfortunately doesn't have separate chapters on Severus Alexander but is worth getting.  Recommend.

The Life of Alexander Severus by R. V. Hopkins is almost a 100 years old and many of the theories presented in this book have been disproved.   It is though a great source of information on Severus Alexander and provides a different viewpoint on various issues.   Recommend if you want to seriously study Severus Alexander.   Hard to get but some companies that print out of print books may be able to print you a copy.