How to add a drop down list next to a free text entry?

There are two ways in which you can approach this. One is to create a dropdown question and add a text box via JS. You'll need to store the value in the text box as an embedded variable. This will be the code for it:
Qualtrics.SurveyEngine.addOnReady(function(){
this.getQuestionContainer().querySelector("select").parentElement.insertAdjacentHTML("afterbegin", '');
document.querySelector("#NextButton").onclick = function () {
input_value = document.getElementById("input_value").value;
Qualtrics.SurveyEngine.setEmbeddedData("input_value", input_value);
}
});

Alternatively, you could create a multiple choice single answer question with your units as choices and then use JS to switch the positions. This will be the code for it:
Qualtrics.SurveyEngine.addOnload(function(){
x = this.getQuestionContainer().querySelectorAll(".LabelWrapper");
x.forEach(item => {
    try{
item.insertAdjacentElement("afterbegin",item.children[1]);
item.children[0].style.width = "60px";
item.parentElement.children[1].hide();
item.children[0].insertAdjacentHTML("afterend","   ");
}
catch(err){
item.parentElement.children[1].remove();
item.parentElement.children[1].remove();
}
});


});


Qualtrics.SurveyEngine.addOnReady(function(){
that = this;
this.getQuestionContainer().querySelectorAll(".TextEntryBox").forEach(item => {
item.oninput = function () {clear_others(item.id)}
});


function clear_others(el){
curr_sel = el.split('~')[2];
that.getQuestionContainer().querySelectorAll(".TextEntryBox").forEach(item => {
if(item.id.split("~")[2] != curr_sel){
item.value = "";
}

});

}
});

The demo for both of them is here. The later option, even though it uses more JS, will provide results, in my opinion, that are more easy to deal with.