Help! Idk what to do

Hello everyone. I have an adopted chihuahua that I got about 3 years ago. I love this dog with everything I have! We were told he was about 1.5 when i got him, and should be around 4 years old now, however, i dont believe thats true as he is super gray! Anyways, Pancho (the dog) is extremlely dog aggressive, he is always trying to bite my parents 90 lb GSD, he has become super timid (just out of no where), he doesnt listen, he has ran away from my boyfriend twice now, where he has had to chase him for 2-3 blocks each time, and he's just been a pain I am a college student, I have a job, plus a 2 year old dachshund. I dont have time to work with this dog anymore, I have tried everything, and I cant take him to puppy classes due to his aggression. I have been considering the option of rehoming him to a slower, older couple that has the time to be with him all day, and has no other pets, (my bfs roomate as a 2 year old dog) and doesnt have different people coming in and out all day. (He has bitten in the past, for no reason!! A lady in my apartment was just walking out the door ) Anyways, I would love your opinions! Do you think this is a good idea? I am having such a hard time even thinking about it, but if its for the better of the dog.. i'm down for it, even though it would break my heart!