I don't know what to tell you really, is there a history of bp in your family? It could also be other things, adhd comes to mind. I would say bring him to a psychiatrist ASAP before he hurts himself.
From what you have said, it is impossible to say, definately need to see doctor. However, my son went through that and more. I took him to behavioral modification therapist, play therapist, allergy doctor, and even an herbal doctor. Finally at age 4 we saw a neuropsychologist and it was determined then that he had bipolar disorder. There is a book The Bipolar Child - The Definitive and Reassuring Guide to Childhood's Most Misunderstood Disorder by Demitri Papolos that is amazing and informative. Talks about different mother's comparing pregnancy to child as infant to toddler and so on. Just don't read the book to try to convince yourself your child has bipolar disorder, but a great read to compare and truly understand.
Since you say he is hurting himself with biting and such, then I say that you need to see a doctor concerning this. It may not be bipolar but some other issue. You say he refuses to use the toilet. Was he potty trained previously? If he was and suddenly stopped also discuss this with your doctor. If not, then maybe he's just not ready for the potty.
The best thing you can do it see a doctor.
he could have other problems like ADD. He needs to be evaluated by a behavorialist. Any changes in his life could causes these things to happen or he could even have a physical problem like cutting his 2 yr molars.
ADD is actually REALLY rare and is the MOST over diagnosed reason to create little drug fiends in America. Don't go that route particularly this early.
If he is BP they may be able to test for it? Is there a history of BP in the family?
More important.What is his family situation? siblings? parents? etc.. Ideally take your doctor to a GP and go from there.
He could have Bipolar Disorder or something else. Quite a few disorders can cause this behavior.
I agree ADD is really not as common as it seems. I think my main concern here is that he is bitting himself. I think for the most part kids have varing degrees of tantrums. My oldest never had a terrible two in his life. Now my baby is going into terrible threes. He really has a temper and is very defiant. He'll fight you until he's blue, that's for sure, and then want to cuddle and play within minutes. Toddlers are really just starting to learn about emotions and expressing themselves.
I think the key is to look at his mile stones and family dynamic. If there is any major stress in the family then he could be acting out on that. That is why it is important to talk to your doctor. We can all speculate but we're not in your life.
I agree that you need to see a doctor. One problem that I have is that children of this age being diagnosed as ADD or ADHD and being put on meds for this could cause real problems. I'm reading the book The Bipolar Child, not because I have a BP child but because I'm BP and feel that I had symptoms as a child. A lot of doctors don't understand or are against diagnosing children w/ BP so instead they diagnose them w/ ADD or ADHD. Also it may not be either of these things at all. Your child may be stressed about something going on around him. Its not something you need to put on here, but to just think about triggers, what triggers the behavior. My step-daughter is anxious, yes she has BP in her family from her birth mother, but I try not to look at her like she is going to be BP. I look at the triggers, when she starts to get anxious I try to avert her attention to something else. She has severe seperation anxiety form her father, I have told him to make a point to tell her when he walks away from her that he will be right back, yes everytime. She is 5, so I understand the levels are different, her mother left her when she was 1, so the circumstances are probably different also. The point I am trying to make is that a lot of times w/ or without BP our kids need our help to be guided to a better way to deal w/ their everyday stresses, however small those stresses may be. How I've learned about these things is through my personal therapy, a lot of my everyday stressors revolve around my 5 yr old stepdaughters strange behavior. It would be a good idea to go see a doctor w/ knowledge on these things. I hope my giant response has helped in some way!