Hi, I'd like to help you with your question.
Psychiatrists as a whole are trained to treat all possible disorders. That includes stress issues such as you are experiencing. One psychiatrist may have more experience than another so when you contact a psychiatrist ask about experience.
Psychiatrists are able to do therapy, but for the most part they prescribe medications to help those who have mental health issues. Master's level and Ph.D therapists do a majority of the talk therapy, referrals and other treatments needed to help people overcome their issues.
It sounds like you are experiencing caregiver stress also known as caregiver burnout, an increasing problem with the aging population. Symptoms can include
Trouble relaxing even when you have the opportunity
Feeling irritable, overwhelmed and on edge
Trouble sleeping or getting enough rest
Always feeling that you need a break
Getting sick more often than you used to
Depression, anxiety or anger problems
It is good that you are already seeking therapy and medications to help you cope. But there are other resources for you to use to help.
One, is there a Department of Aging near you? If so, they can offer companions, financial assistance, Meals on Wheels and other helpful services. Contact your local United Way for information.
Two, support groups on line and in person can provide you with someone to talk with who understands your stress and also they can offer resources you may not be aware of.
Three, accept help when it is offered. Caring for someone is a huge responsibility but when it is a parent we are caring for, we tend to feel guilty when we need a break. But you can be a better caregiver to your mother if you are better rested and can have time to care for your own needs as well.
Four, remember to do basic things for yourself. Eat well, exercise, laugh, and get as much sleep as you can. If you can afford to, hire someone to clean your home at least once in a while. It will give you a break and make you feel better.
Here are resources that can help you further:
The Emotional Survival Guide for Caregivers: Looking After Yourself and Your Family While Helping an Aging Parent by Barry J. Jacobs
The Caregiver's Survival Handbook (Revised): Caring for Your Aging Parents Without Losing Yourself by Alexis Abramson and Mary Anne Dunkin
You can find these books on Amazon.com or your local library may have them for you.
Let me know if I can help any further,