Awww *hugs* for kitten, he's still morning the loss of his friend.
My CW passed a few months ago and his brother/litter mate Zorro was very distraught when it happened, still isn't 100% back to his normal self. He was the active one of the two (I call him my ADD kitty because nothing can hold his attention more than for 2-3 minutes tops). He became very anti-social, spending most of his days sleeping/hiding, I think he put on a pound or two, and he's a black & white cat and he started getting "grey" hairs in his black fur. He'd walk around the house crying for him, and Zorro was the quite one never made a peep, his big brother was the noisy one of the two. When he showed no interest in things he normally loved, like being toted around the house over your shoulder, licking my dads head/hair, ect it made us so sad and depressed. We also went threw cuddle withdrawals because both of them were big cuddlers. Keep giving him extra love and TLC when he lets you. After loosing two dogs so quickly I don't blame you for being extra anxious over this, I would be too.
If your not ready for a new kitten in the house I'd say hold off on it until you feel good about it. We got a new brother for Zorro and they started off really good until they were together 24/7. Zorro got super stressed out by the new guy, he'd rub up against him and purr on him and he didn't like it one bit. He would run away from the new guy! They are better now but they still get scrappy. Zorro is a lot better now, not 100% back to his usual personality but major shifts in the right direction. He's more snugly again, wanting to be carried around the house again, and licking my dad's head/hair. So that's another thing to consider before jumping into getting a new friend. They may not hit it off and it could cause more stress on your kitty.
I wish I could give you some better advice on how to help your kitty. Since you took him in for a check up recently, maybe you could call the vet and ask if they have any tips to help your grieving kitty. When we started looking for a new kitten, our vet gave us a ton of tips (several pages worth of info)on how to help introduce them to each other, along with shelters to check out.