At the hospital they do not need consent to run a test on a patient in an emergency case, they almost always do. After the child was unconscious, the child does not know what it has or has not ingested, it does not know it's allergic reactions, and it cant give a reliable account of the events. When a child is brought for treatment there are three possibilities really. 1. Child abuse
2. Child neglect or 3 that the child sustained the injury in some way that was unforgeable, that a reasonable guardian might not notice. In many cases the hospital is required to forward information to police, since the child may not know exactly what happened, and at that point the parents are potential suspects and may not be truthful in an attempt to minimize their part, I am NOT saying this is what happened, I am saying this is what the medical staff is faced with, and they have to make the decision based on their knowledge and training. People can make mistakes and lie, a test is much more accurate, a test doesn't care what happened or who did what, it is completely neutral, it can be done improperly and that can be challenged in court, but generally they are more reliable.
I do feel for your situation and i do believe you meant no harm that this is a tragic accident. As a parent it is very hard to remain objective and emotions can cloud the picture. that doesn't help anyone, your more likely to make a mistake or say something you may later regret, as things can be twisted and manipulated.
If any when you are arrested, if you can not afford an attorney, the judge will appoint one or assign the case to the public defenders office and they will handle the defense. If they are going to arrest you then they are going to, there won't be much you can do to stop it, the best thing is damage control, not to further incriminate yourself unintentionally. If you speak to the police without an attorney present you may have waived all your rights within the first hour, they are tricksters. The hardest thing to do is to patiently wait for them to get arrest warrants and come to your home, if you have family local who your children can stay with, that would be good, as it will be even more traumatic on them.