GEE filter image to month before specified date

I am using a for loop in GEE to loop over several years of data adding bands to an image (MODIS fire data). I am currently adding a band for the mean NDVI in the month the fire occurred and the previous month. However, I am struggling to get it to work for adding it to the previous month. I have used ee.Algorithms.if() so that the previous month will be 12 if it is currently 1 (so goes from January to December) and that the year becomes the previous year if the current month is January.

Make collection of NDVI with mean monthly values:

// currently values for every 16 days, take the monthly average
var month_mean = ee.List.sequence(0, 20*12).map(function(n) { // .sequence: number of years from starting year to present (Jan 2001 to Jan 2020)
  var start = ee.Date('2001-01-01').advance(n, 'month'); // Starting date
  var end = start.advance(1, 'month'); // Step by each iteration

  return ee.ImageCollection("MODIS/006/MOD13A2").select("NDVI")
        .filterDate(start, end)
        .mean()
        .set('system:time_start', start.millis());
});
//print(month_mean); 

var meanMODINDVI = ee.ImageCollection(month_mean);

Set parameters for filtering image collections:

var startMonth = 1;
var endMonth = 12;
var startYear = 2018;
var endYear = 2019;
var d = 1;
var m = 1;
var y = 2018;

 for (y; y <= endYear; y++){
for(m; m <=endMonth; m++){

//// filter fire data
var fire = ee.Image(fireCCI.filterDate(y+'-'+m+'-'+d).mosaic());
///// NDVI at time of burn
var modisNDVI = ee.Image(meanMODINDVI.filterDate(y+'-'+m+'-'+d).mosaic());
/// NDVI month previous
var j = ee.Algorithms.If(m==1, 12, m-1);
var k = ee.Algorithms.If(m==1, y-1, y);

var modisNDVIprev = ee.Image(meanMODINDVI.filterDate(k+'-'+j+'-'+d).mosaic());

var fireImageAddDate = fire.addBands(modisNDVI)
                            .addBands(modisNDVIprev)
                            .setMulti({"day":d,"month":m,"year":y});
var fireImageWithDate = ee.Image(fireImageAddDate);
}}

If I print j and k they will print the correct values, but as they are a computed object I get this error with trying to run the code:

NDVI previous month: Layer error: DateRange: Bad date/time 'ee.ComputedObject({
  "type": "Invocation",
  "arguments": {
    "condition": false,
    "trueCase": 2017,
    "falseCase": 2018
  },
  "functionName": "If"
})-ee.Number({
  "type": "Invocation",
  "arguments": {
    "condition": false,
    "trueCase": 12,
    "falseCase": 5
  },
  "functionName": "If"
})-1'. 

I have tried casting the values using ee.Number() and ee.String() but still get the same error messages.

// currently values for every 16 days, take the monthly average
        // .sequence: number of years from starting year to present (Jan 2001 to Jan 2020)
var month_mean = ee.List.sequence(0, 20*12).map(function(n) { 
  var start = ee.Date('2001-01-01').advance(n, 'month'); // Starting date
  var end = start.advance(1, 'month'); // Step by each iteration
  var prev = start.advance(-1, 'month'); // previous data

  var currentImg = ee.ImageCollection("MODIS/006/MOD13A2").select("NDVI")
        .filterDate(start, end)
        .mean()
        .set('system:time_start', start.millis());
  var previousImg = ee.ImageCollection("MODIS/006/MOD13A2").select("NDVI")
        .filterDate(prev, start)
        .mean()
        .set('system:time_start', start.millis());
  
  var imgToReturn = currentImg.addBands(previousImg)
                            // .addBands(YOUR_FIRE_IMAGE)
                            .setMulti({"day": start.get('day'),
                                        "month":  start.get('month'),
                                        "year": start.get('year')})
  return imgToReturn
});