I don’t like to discourage people who exercise just once a week, but this small fraction of exercise is not going to give you the benefits you want, whether it be strength, more muscle, fat loss, or flexibility.
There are seven granddaddy laws of training, one being the General Adaptation Principle, which states that a once a week full body workout, and/or training a body part once is a week “is generally not advised as it is far too infrequent and too much rest has expired (1)”. If you are too exhausted from that one workout to exercise again 2-3 days later, maybe because you’re new to training, or you worked out really hard, that’s normal; it’s your body’s built-in mechanism protecting you against injury.
You don’t need to push through the pain, that’s never a good idea. What you want to do is switch up your workouts, so that some are high-intensity and others are low-intensity, and do different types of exercises. For instance, two days a week I lift heavy for an hour each; two days a week, I practice yoga or do cardio between 30-60 minutes depending on how I feel; and two days a week I do moderate-intensity bodyweight and/or band exercises. I take Sundays off to recover and rest.
In conclusion, exercise all muscles twice a week with varying intensity for maximum results. With consistency and variety, those workouts will get easier, you’ll get stronger, and you’ll have to make it more difficult to progress to the next level.
(1). Source: Hatfield PhD., Frederic. Fitness: the Complete Guide. Carpinteria: International Sports Sciences Association. 9th ed., 2018. Print. Pgs. 417-419.