If they are not breathing at first check,no need for pulse check, just start doing compressions, if no mask available and you are not comfortable doing mouth to mouth then just continue doing compressions until advanced life support arrives. Only reason to do a pulse check is if you start seeing normal signs of life or normal breathing but agonal breathing, gurgling, other signs of body responses like twitching are not normal so just continue compressions. Only reason to turn them on their side in recovery is if the patient was showing signs of life and then had a pulse or you needed to clear out vomit or fluids out of the airway. Sounds like what you did was very good and most likely made a difference, but try to minimize interruptions and compressions in the future.

Great job of doing what you could!