Is anesthesiology still a good profession to get into?

Yes. It is a very rewarding profession. I can tell from my own experience as a anesthesiologist.
Yes. There are still shortages of all physicians across the country in all specialities. The population is expanding, the baby boomers are getting sick. There will always be a need for anesthesiologists and all physicians. This is also a portable profession, much like engineering, should you wish to try your luck in a new country.
Of course . Anesthesiology requires broad understanding of medicine. Anesthesiologists are very educated and fun to have around. Anesthesia includes many sub specialties , which allows you to do procedures, take care of critically ill, treat pain, etc. Or manage your practice. Your happiness will be determined by how good you are as anesthesiologist.