The symptoms you describe, leaking a large volume with increased pressure put on the bladder with coughing, sneezing, etc. is consistent with stress urinary incontinence. However, you also describe not being able to make it to the bathroom without leaking which is consistent with urinary urge incontinence (also called an overactive bladder). When these two types of incontinence are present in the same patient, it is called mixed urinary incontinence.
The key to optimizing treatment for Mixed Urinary Incontinence is to have an appropriate assessment that determines why the bladder is not functioning properly. A physician with experience in treating women with bladder issues will be able to perform such an assessment and then tailor the treatment to your specific symptoms and goals.