From looking it up, it appears that the Baker Act is a Florida-specific involuntary institutionalization in a psychiatric hospital.
So I think that it can safely be said that many of us on this site have had their child committed to a stay in a psychiatric hospital or other psych setting. Some families have had to make the difficult decision to put their child in a hospital, and some have had those decisions made for them by law enforcement officers or doctors. Some of the stays were very brief, and some were long.
During a couple of really serious medical crises in my daughter's life, we experienced this. Once she was placed in a locked down ward in a psych hospital.
But regardless of what's it's called - Baker Act, 5150, committed - there are some things in common that have to happen. Maybe it's medication, or a medication change, or stopping a certain medication. Maybe it's help for the patient, or maybe it's help for the family. Maybe it's tools that are given (not actual tools, but skills and methods) so that the home situation improves. Maybe it's outpatient counseling, for everyone. But it's obvious that the current situation needs to change. And it's not always the patient. Sometimes it's the parents or family members that are causing the child harm or pain.
There's a reason that your son is so hurting. You've written about school difficulties, neglect from your boyfriend, and a difficult situation at home. Most psych hospitals will have a family meeting. Figure out why he hurts. Make sure you listen and take notes when the doctors talk to you. And if there are suggestions, follow through on them.
I'm sure you love him and want him back at home, but please make sure he doesn't come home to the exact same circumstances that caused this situation. Make the brave changes. Get him (and you) continued counseling.