What do you envision yourself doing? Don't look at it as choosing a "career." People change jobs all the time in the social work field - following the grant funding to different organizations, or going to gov't positions.
A position that I imagine pays fairly well is working in hospitals. When a patient gets discharged but is not ready to go home, there are various facilities they go to - skilled nursing facilities, long term acute care facilities, etc. The hospital has a person coordinating all this. Not sure if they are nurses - I think some are. Hospice facilities also tend to have social workers. So, not all social work is going to be at the lower end of the pay scale. But, a lot of it is.
Nowadays, people change jobs every 2-5 years. You can move between different things. Heck, you could start out in social work and find your way into a professional fundraiser position for a non-profit. When you start working, keep your resume current, and learn how to use "transferable skills" to sell yourself for the next position. It's all about PEOPLE, confidentiality, getting people to open up to you and trust you, getting them to be receptive to your ideas, documentation, more documentation, etc.
Right now you just need to choose a major. Look at both degree plans. Take the classes that will count for both, while you think this through. I don't know anything about psychology. My degree was sociology, not social work. I worked 25 yrs as a police officer and then 10 as an employment counselor at the state workforce office. That second job didn't pay hardly anything.
Recommend further looking at the various types of work people with both majors actually do - you will be surprised! See if the school has info like that on its graduates.
Getting a Ph.D will allow you the opportunity to teach, and possibly allow for more opportunities later if you are interested in lecturing at seminars (I do regret I didn't make this choice for that reason). LCSW's can do a lot of the same things as a Psychologist, they can have their own practices, counsel, work for companies, consult, etc. I can't tell you that you will always make more money in one or the other. It honestly depends on what you want to get into. You don't have to get a Ph.D to work in Psychology, but it does help. A Master's in Psychology won't afford you the same opportunities.
It's not always about pay, you do need to find work that nourishes your soul. So you don't experience burnout. My advice, intern, find great internships. It will help you figure out what you like the most. Good luck!
Compensation is not be underestimated as a component of job satisfaction. We all have to pay the bills. Some of us have different circumstances as well. If a grad has the benefit of their parents covering their education and first-car bills, they could be $70-$150K ahead of someone who didn't have any help at all. A $100K of debt at 5% for 10 years equates to a $1,000 monthly payment for student debt. Factor in living expenses in an expensive city, some college grads won't have the option of social work. So one practical question and exercise, is can you afford to do an entry-level social worker role for $30-$40K/yr.
I'll offer two other generalities:
1) I do buy into the fact that most people will be most successful (and thus have a greater life-satisfaction and earn higher wages) when they align their careers with what they ENJOY and they ARE GOOD at doing. Sometimes, those considerations don't overlap. But, if you can be an amazing social worker, you may find yourself (should you choose) raising through the ranks to higher salaried management positions as well.
2) people can make it work. or, where there's a will, there's a way. if you find something you really enjoy, you probably won't mind making the sacrifices on living with a roommate in a smaller place and taking longer commutes on public transportation to reduce your monthly expenses. These are trade-offs you may be more than with making, because you enjoy the lower paying job so much more.