Unfortunately, biting is a normal phase that many toddlers go through. Most doctors would not diagnose a 2 year old with ADHD, especially since many of the "symptoms" of ADHD are typical 2 year old behaviors.
There have been many changes in her life, and that can certainly contribute. Play therapy certainly couldn't hurt, but probably isn't necessary. Instead, family members should be taking time to give her 1 on 1 attention every day. If she is climbing things she shouldn't, then you should be giving her opportunities to climb on things that are acceptable. This is a normal and necessary outlet for young children. When my daughter was 15 months old and started climbing on everything, i brought in one of the small plastic little tykes climbers from the yard and put it in her playroom. If she started to climb on furniture, I simply said "We climb on the climber" and she quickly learned. I also made sure to take her outside whenever possible, and to parks to get the energy out.
She sounds more like an energetic 2 year old who needs attention and an outlet for energy than a child with a disorder.
As for the biting in school, that mostly falls on the school since you are not there. They need to be providing her with sensory activities (water, play doh, sand play) as that often helps. They need to make sure there aren't too many kids in 1 play area and there are plenty of toys to spread the kids out. They need to model using words when frustrated ("I don't like that!" "Stop!" etc...) and they need to anticipate when there may be a problem so that they can make sure a staff member is nearby. For example, if she always bites when lining up, then they can put her at the end of the line by an aide. This is a typical phase and it should pass, especially if you give her the attention and outlets she needs at home.
you can ask the school to document the biting incidents to see if there is a pattern.
Absolutley agree with tiredbuthappy, what you have told us here seems to be normal child behavior after having a new sibling..many go through the biting phase they don't have disorders ..
I would say first of all that biting is completely normal or frequent at this age. I think it comes out of frustration, at least from my daughter who does the same.
I once asked my pediatrician about what to do and he said try to distract her when she is about to bite and not to give it much attention for it to not become an issue.
What I do for example is put her down if I´m holding her or remove her from his brothers side when she tries to bite him.
My son went through a biting phase. He is also a total daredevil...part mountaingoat I think..lol. I worked really closely with his daycare and we made sure we were consistent in what we were doing. They watched him closer and if frustration or even anger were obvious, they would distract him with something else. When he would bite at home, I would say firmly (without yelling) "your mad" or "your sad". "It's ok to be mad/sad, but it's not ok to bite. Biting hurts mommy." "Mommy won't play with you when you bite". Every day that I picked him up, I would ask in a very exaggerated tone "how was Ryder's day today". If no biting, he would get a small toy (I picked up a bunch of little things at the dollar store, and carried them with me). Again, I was very very consistent. I am happy to say he hasn't bitten in over a month. He is active, busy and a climber, but he is not ADD. He also didn't require therapy for this, just consistency and being firm. And keeping calm with him was super important.
Many kids go through a biting phase. My DD just bit herself when she went through that phase...I guess that's a good thing? I remember biting my siblings when I was little. I think an ADHD dx and Psychological Play Therapy with a certified therapist is taking it a little too far. Don't overreact. It will only reinforce her behavior because you are giving her biting so much attention.