Clairgod, word for word, I could have posted your question when my first son was 18 months old. He's now 7 and his liveliness is still at times a problem for us all, but he is happily settled at school and learning well.
I can't give you better advice than Sml on additives, so here are some other thoughts.
Get his hearing checked to see if the reason he can't settle is anything to do with this. And continue to keep tabs on this. My son had a mild and temporary hearing problem which definitely affected his ability to concentrate.
I found it really tricky to decide if my son was hyperactive or just lively. To be honest, the jury's still out! He did sleep well, both at night and for naps during the day. In the doctor's mind, this tended to rule out hyperactivity. We also avoided additives, but not slavishly, I have to admit.
I made a real point of gathering opinions about my son from people who had lots of experience of young children, and who knew my son well. eg: friends of the family who were teachers and social workers, also my son's babysitters. This all helped me get a better perspective on
things and get some informal support.
Just a suggestion, if you do not have a babysitter, local nursery nurses often do babysitting on the side. You could contact a local college, as I did, and find a highly trained babysitter this way who, as well as babysitting, can offer a good insight into whether your son is hyper or merely lively.
Also, if you have not already done so, ask all grandparents what you and your partner were like as toddlers. My husband was apparently just like my son. He mostly grew out of it, as my son is doing. Knowing this helped a lot.And keeping with families, are you and your partner both more active than average? Dh and I are, so how can we be surprised that our son is too?
But we still keep monitoring the situation.
He was at his most lively from the age of 2 to 3 and a half years, then he began to calm down. So perhaps you better brace yourself for an action-packed time!