1. The other person has to be willing. Unfortunately, no matter how dysfunctional we think that a person or situation is, people never change until life doesn't work for them anymore. You can have the best of intentions and think that things would be better if the other person just did this or that or the other thing. It has to be their idea - not yours - or they will never totally buy into the plan.
2. They need to set their own appointment. When you schedule an appointment for another person then you can be setting yourself up for trouble. The other person might be angry with you and embarrassed that you have shared information about their situation with someone else. Better to let them book their own appointment and then they will likely be more committed to attend and participate.
3. Therapy is not magic. Just because someone goes to see a psychologist of psychiatrist does not mean that they will change. They might not participate in the process! If it took years to get into trouble, one or two appointments won't resolve everything. Some people claim that they tried therapy and it didn't work but they either didn't engage, quit right after they started or really didn't want to change in the first place.
4. No one can force another person to get treatment unless high risk is assessed by professionals (not you). Do not be frustrated when a health professional will not talk with you about another adult's progress or think that the person who you care about will be locked up until they improve. As professionals we need to respect confidentiality and free will when it comes to treating individuals. And even adolescents let their feet do the talking for them sometimes. Each of us has the right to consent and the ability to participate or reject services no matter what another person thinks is in their best interest.
5. The person who called may benefit most from getting help. Maybe you need help in dealing with your anxiety or need to learn to let go of things that you cannot change. Over the years, for example, I have met many people who live with someone who has an active addiction. They think that if the other person just quits using substances than life would be good. Well, first of all, you can't make someone else do what you want. If they do quit using, things will change a lot and perhaps you wouldn't adapt well. Better to focus on what you need than on wishful thinking!
It is all about focus. Invest your time, energy and money on ensuring that you are healthy and happy. I am not saying that you shouldn't care about others or try to help but like Kenny Rogers once sang:
"You gotta know when to hold 'em; know when to fold 'em. Know when to walk away. Know when to run!"