Exactly. One can go into nursing with a BSN, and can choose to get an advanced degree later if one wants to be, say, a psychiatric NP (masters or doctorate level), a clinical nurse specialist, etc. There are many advanced nursing degrees. But, as @Twoin18 has stated, often the hours and the demand in hospital nursing (ambulatory surgery centers might be demanding too, but the hours are better) can be extremely stressful. And I am familiar with nurses who have had injuries from lifting/repositioning/transferring patients. And you also want to be sure you are comfortable with the… um.. “less glamorous” aspects of nursing (think bodily function, etc).
With a psych undergrad degree, you can get a hospital job like a mental health assistant/associate (some states might require licensure but if so, its probably uncommon), but if you want to provide a higher level of care, you will need an advanced degree (masters or doctorate). It can be in a variety of areas of psychology (clinical, counseling, educational, industrial/organizational, etc), but you can also get a degree in social work, and with some of the terminal masters degrees in counseling or social work you can still be licensed in several states and have a very lucrative career.