Karen,
I'm going to write a short novel here, please bare with me.
In my opinion you've answered the question that is the key to Alex's issues. Low Testosterone and my thoughts would suggest elevated Estrogen (estradiol) in his system as well. I would like to convey how "important" testosterone is to the male system. It effects EVERYTHING in the male system. I'm going to give an excerpt from some "light" reading I've done on the matter:
"Common symptoms also include depression, mental fogginess/fuzziness, difficulty concentrating, anxiety, loss of muscle, increased weight gain, decreased facial hair and a general feeling of not caring about anything. When you are low on testosterone, you often just don't care about anything - you just "exist". Pleasure and desire can be greatly decreased greatly affecting your career and your relationships."
Sound familiar?
"Normal" range of testosterone in the male body is between 260-800 ng/dL however understand that 260 is a VERY low reading and even this low will affect how any man functions. My readings my first test was 70 ng/dL...I was a mess. My idiot GP put me on 3x the normal dosage of androderm to get me back to "normal" and that caused massive issues. Ever read an Incredible Hulk comic or seen the movies? That's when I understood and fully grasped how delicate and important those levels were for me or any man really.
When you start testosterone "replacement" therapy, your body will stop producing the hormone naturally so it's EXTREMELY important to be consistent with Low T therapy and have a dosage that keeps Alex at a consistent 500 ng/dL level in his body. This will keep his moods stable. We've all heard the expression for women when they get their moodswings as "hormonal"...well it's true for men too we just don't like to admit it or understand it.

Personally as I've shared I can test REALLLLLYYYY low on T levels however I discontinued the replacement therapy as it was difficult to maintain even levels so my moods were all over the place. I found that through diet, exercise and some other tricks I can keep myself consistant. I'd like to share some thoughts and those tips here.
EXERCISE: Even if Alex is on testosterone replacement, exercise will help his moods. Testosterone serves several purposes in the body, one of the most important is muscle building and if he's building or using muscles he's using that testosterone as opposed to having excessive free testosterone in his body which will cause swings on the really high side or rages in some people (me!). Exercise will also help on the self image, I may be disfigured but from the neck down I look phenomenal (if I do say so myself and I do!) and that helps my confidence, gives me the swagger to do what I do.
DIET: I'm almost completely on a liquid diet and I do just fine with it. I only eat solids when I'm "highly" motivated (mj reference) so anymore that's about never. What I've found is that through juicing, supplements and Ensure I can give my body everything it needs to run at a high pace. If you know anything about my lifestyle I run hard. I work long hours (average over 80 per week) and exercise hard so my body gets the fuel it needs to keep going. Diet will also effect testosterone levels and therefore your moods. I balance my protien intake (.55g/lb of body weight) as excessive protien in your system will lower testosterone levels and I distribute them throughout the day to get my body into protien synthesis (converting protien to muscle). 3 meals out of 5-6 has to have 30g of protien to do that. The more muscle the more T. I use a whey protien powder for most of my protien intake as it's easy and mixes well with Ensure.
Fats, if you've ever heard about the "Greek Physique" (greek god statues, etc...) they actually attribute that to Olive Oil. Fact is the more good fat you have in your system the more T you will produce. Olive Oil has 14g of fat per "tablespoon" and 140 calories, it is a phenomenal supplement to Ensure. Cocunut Milk and Peanut butter you can use as well, I use all three throughout my day. Most of us on liquid based diets lack good fat so we will lack T as well if not addressed.
Supplements: Horny Goat Weed, Ginseng (I use Korean) will up T production and help sex drive! Yohimbe you can use as well..it has amazing benefits but has interactions with MAOI's and has other effects you have to be careful with. It works well though as it increases blood flow to the male and female sex organs. I use all three but I'm very careful with the Yohimbe and only break it out on "special" occasions

SEX and sexual organs: There is a reason why testicles sound a lot like testosterone...they are important! Not only do you have to make sure they see regular duty but you also have to make sure they are in an environment to thrive! Unless Alex is exercising he needs to keep the boys hanging...boxers baby. Keeping those guys cool and free will help testosterone and normal sexual function.
Sex is very important to any guy. He needs to get excited, best to do so in the morning and that will promote a good outlook all day. The reason...testosterone! Does it for women too actually. When a man's excited he will transmit T through both saliva and semen to his partner giving them the added bonus too. Endorphans aren't the only cause of well being after sex

testosterone is a magic thing. Even if you are too worn out for it, there is always other means and as adults we need to understand there is nothing wrong with masturbation or getting sexually aroused. As with anything though there has to be balance and boundaries.
Anyway what I found for myself through these tips is I've been able to get my 70ng/dL testosterone reading to a healthy 450+ level natually, consistantly and that has evened out my moods, given me a fantastic outlook with the added benefits of looking and feeling amazing.
Sorry for the novel, hope it helps.
Live life, be well
Eric