Medication for aggressive dog?

Hi! We adopted a 2.5 year old male white shepherd/lab, Denver, almost a year ago. At the time, he had already had two homes and been returned to the shelter from both, but we were told it was just that he was too large and active. We now are sure that it was because of his aggression. Denver loves us and our other dog. He can be very affectionate (although he never cuddles with us or typically keeps to himself) and he loves to play with us and go for walks and car rides. Despite the fact that he clearly loves us, our friends, and family and seems like a very happy dog, Denver can unpredictably be very aggressive.

His aggression has decreased dramatically since we got him, but it is still definitely there. When we first got him, if we walked into a room straight toward him, he would run out and jump up and bite us. When he bit though, he did not chomp down as hard as he could. It was almost more of a frantic barking and snapping at us. Now, attempting to bite is more rare, but he still does at times. More often he growls as if he would bite, but stops and puts himself in his "time-out" spot. It happens most often when we walk past his dog bed or approach him when he is under a table or behind a couch. We also know that if we tried to reach down and pet him unexpectedly, he would probably take our hand off. We have noticed a recent increase in aggressive behavior and the only change in his routine that we can think of us is that he has had a little less outdoor activity. He is very friendly and sweet with people he knows, but whenever a new man comes to the door, he growls and tries to bite him. He has no problem with women though. Occasionally, he will growl when he thinks someone is going to take his toy or bone, but that is not common for him. We have tried training him ourselves using treats, spraying water, and "time-outs". It wasn't that we were lazy or didn't want to spend money on training-we were terrified to bring him anywhere. Training him has definitely made a huge difference, but we are still worried about him biting someone. Especially since a few times he has just freaked out and tried to bite for no reason at all. We are wondering if he might have a chemical imbalance or anxiety disorder and if he might benefit from medication. Does it sound to you like he might have some sort of medical problem? Thanks!