You need to be very careful in disclosing any information about mental illness beyond "I am going through some stuff right now".
Plenty of people will tell you about all the various and sundry laws protecting people from discrimination, and yes those laws are in fact on the books.
What they don't tell you is just how ineffective they are, or how much effort you need to put in to get them enforced. From first hand experience, I can tell you that this is not good for your mental health.
While a company cannot legally fire you for having mental illness, they can fire you for violating some obscure company policy. The more clever (or evil) companies have managed to deliberately craft some policies that are both vaguely defined, in scope, and consequence, with phrases such as "or at the discretion of..."
Or, in other words, if they want to get rid of you, they can find a way.
I have Asperger's/autism, and severe panic disorder, and have had what are called "pseudo seizures" due to it.
The more you can keep this out of the workplace, the better for you. If you need to take the occasional day off to get help, or to just regenerate, do it. If you are seeing a counselor or psychiatrist, see about upping the visits, go to more meetings of support groups (there are free ones out there) and do what you need to do to protect your performance.
Even when you are there long enough to qualify for FMLA, try to avoid it, because, again, legally they can't fire you for that, but they can find other reasons.
Now, this may sound contradictory to everything I've said so far, but:
If you think that this is going to start affecting your performance,
GO TO HR BEFORE ANY DIPS IN PERFORMANCE OR OTHER ISSUES ARISE
The various laws do not protect you if you bring up disabilities AFTER disciplinary actions are being taken, and you won't get far.
Sadly, people abuse the system, and if you go to them after issues arise, they will tend to make that assumption.
HR may be able to direct you to additional resources, but make sure you do as much work on your own first
If you need to go to HR, you want to have a long list of things you've tried to do before involving them. Notes from your doctor, any medications you are taking, preventative measures and/or steps you are taking to ameliorate your difficulties, et cet. This will show them the genuine effort that you've put forth and make them more likely to assist you. Again, because of people who game the system, you want to show that you are not one of those people.