I don’t find two handed swings to be especially ergonomic. I have trouble fitting both of my moderately large hands together in the kettlebell handle and, when I do so, my wrists often end up being cocked at an unnatural angle.
I do one-handed swings instead. One handed swings allow me to keep my both my elbow and wrist straight.
It might be worth trying one-handed swings to see if you find them to be more elbow friendly.
It occurs to me too that your volume (number of repetitions) might be too high. I don’t work out to videos, but am under the impression that they’re fairly high in volume often with fairly light weights. You might consider increasing the weight of the kettlebell that you’re using, but drastically lowering the total number of reps. (Or, if you’re starting out again, just use your existing kettlebell until you get back into it.)
Something else to look at is foam rolling / myofascial release / trigger point therapy of tissue near the elbow. For this area, a LaCrosse ball is often a better implement to use than a foam roller. If you find the right spot to massage, this will often fix your elbow pain. The book that I recommend for Trigger Point Therapy is The Trigger Point Therapy Workbook: Your Self-Treatment Guide for Pain Relief by Clair and Amber Davies. Elbow pain can also be treated with a technique called “Voodoo Flossing” which is described in Becoming a Supple Leopard 2nd Edition: The Ultimate Guide to Resolving Pain, Preventing Injury, and Optimizing Athletic Performance by Dr Kelly Starrett and Glen Cordoza.