I had been on Flexeril, not every day (Cyclobenzaprine) for years and no hair loss (I recently was switched to another muscle relaxant....Flexeril can cause short term memory loss..I surely don't need that!). I will say the following caused hair loss for me:

1) I lost a lot of weight in 2016 and quickly....
2) I had an intense surgery in 2016
3) I started with Thyroid disease (unknowingly) at the end of 2016.

The combination of all of these caused extreme hair loss. I was not getting enough fat in the diet I was on or carbs, surgery/anesthesia puts a lot of stress on your body & thyroid disease causes hair loss. It took several months for it to stop extreme shedding. I am not versed on Gabapentin so I can't say. Stress & Covid can cause hair loss as well. It's traumatic when your hair starts coming out. Praying for you...I understand.