[SalesForce] Show validation rule error next to the multiple field

Yes, we can specify where the error message would be displayed. But this applies to standard layouts and not to the custom developed visualforce pages. You need to change your function as to make it work:

public PageReference doSave() {
try{
    update links;
}catch(Exception e){
  ApexPages.addMessages(e);
  }
}

This will redirect validation messages to visualforce page. The errors would be displayed at the location of <apex:pagemessages /> tag

Please try this:

Ltng Cmp:

<ui:inputSelect value="{!v.sobjectType.Picklist}"
                        label="Picklist label: " class="dynamic" 
                        aura:id="pickList"/>
<ui:inputTextArea value="{!v.sobjectType.Field}" 
                         class="slds-input" label="Text area label:" 
                         maxlength="200" aura:id="textArea" />
<lightning:button label="Submit" class="slds-m-top--medium"
                                      variant="brand"
                                      onclick="{!c.clickCreate}"/>

Ltng Controller JS

clickCreate: function(component, event, helper){
       if(helper.validateForm(component)){
          /* Do record creation */    
    }
}

Ltng Helper JS

validateForm: function(component){
        var validData = true; //Flag
        var pklstField = component.find(“pickList”);
        var pklstFieldData = pklstField.get("v.value");
        var txareaField = component.find(“textArea”);
        var txareaFieldData = txareaField.get("v.value");

    if( pklstFieldData == “Picklist value” && txareaFieldData == null){
        validData = false;
        txareaField.set("v.errors", [{message:”Text area cannot be empty.”}]);
    } else {
        txareaField.set("v.errors", null);
    }
 return validData;
}