Your peak heat load is not on the worse month, it is on the worst part of the coldest night. Basically when the temperature is the lowest that it you expect it to be. It is the 99% heating load temperature. You can use a search engine and find the temperature for your region. I live where the 99% temp is -20f. Your average is not going to tell you anything if it is based on the average for the month and sun is factored in. At night you don't have sun and if you wake up and the sun isn't up yet you might be cold. The average for January where I live was 11f but the coldest night was -20f and we had about 10 nights where it was in the negative single digits getting close to -10f. If your average for a month is 18750BTU/hr you might get a ballpark figure for finding the weather temperature average for the month and doing some monkey math to the coldest temperature you would expect by the difference in temperature from average to the coldest expected. If your average is 18750/hr be sure you factored in the efficiency of your current equipment versus the new equipment too.
The way I calculated the load with my house is I monitored the run time for the 9 hour period where the temperature was in the -20f region last year on January 21st. I basically paid attention to the forecast for the coldest days and logged the on-off of the call for heat which is very close to the time the gas valve is operating and then did the math for the duration it was on divided by the total amount of time I was logging and multiplied that duty cycle percentage against the output rating of my furnace. That day I calculated 27700 BTU/hr would be required. There was no sun at the time so that was no factor and I had to play with the numbers a little bit as it was -15f for part of the calculation and my house wasn't quite 72 degrees which is what you are supposed to calculate to but once I did the math, I realized that the smallest condensing natural gas furnace I can buy is 40k BTU/hr furnace. Later on a -10f night I raised the house to 80 and calculated then too and the numbers were higher but nothing a 40k BTU/hr furnace couldn't handle. Keep in mind though that my results would be different than yours because I've been insulating and air sealing to get my numbers and my 1985 house wasn't too bad on insulation to begin with, the air sealing made a big difference though.
The professionals size using an ACCA Manual J calculation. There are some heat load calculators on the net but none that I've really liked much so far. Some of the ones that I've had pros recommend to me that are accessible to non-pros. Of course you can download the spreadsheet from here but the details on how to properly fill it out are in the book that is available to $74.95 for mortals and $52.49 for those in the anti-DIY club. I've considered buying the book, then found it was checked in at the central Minneapolis library but I went there and apparently it may have been stolen or maliciously moved to a location it shouldn't be by an HVAC contractor.
Spreadsheets
https://www.acca.org/industry/system-design/speedsheets
Instructions
https://www.acca.org/store/product.php?pid=30