May I ask why would he have to beg for a band aid ? Sometimes it works better if you can accommodate the child,.where possible and my opinion is that tantrums very often can be averted,with distraction or simply ignoring him . To know if he has any disorder or nutritional imbalance it would be best to speak the doctor .Good luck
I agree with Margy. Some kids have a strong desire to put bandaids on stuff, and those parents buy their kids bandaids like others buy bubblegum.
He sounds like he has anxiety to me, or is brushed with a little compulsiveness, and he really needs certain things to maintain his level of calm.
Are the other things he asks for as benign as a bandaid? At this point, I wonder if there is a serious need to have all the power on the part of his mother.
It could just be that he knows it pushes his your buttons. Children can act up because they don't like to be told "no". He needs to know that when he is told no that it is final and he's not allowed to whine and moan on and on.
Obviously you don't want to be unreasonable but also if they think they can get their own way by shouting or screaming or even if they are using this to "punish" you because they know it stresses you out and gets your attention then he needs to learn that it won't be tolerated.
The best way to handle it is to make it clear that what they are doing is very naughty and you are angry with them, then walk away - leave them and ignore their behaviour. After he has calmed down make sure there are consequences for what he's done (like withdrawing a favourite toy or making him do a chore) and be consistent. He also must apologise to you for it. Saying he can't control his behaviour is just an excuse I think.
Also praising them when they are told no and just accept it instead of whining or getting angry is a good thing.
BUT if you already do all this and suspect it could be something else, then definitely take him to the doctors. Being able to control your temper is a learning curve for kids but I suppose it could be a symptom of something else (though this is less likely if his behaviour is otherwise unchanged and normal for him).