Generally speaking, the law governing your injuries will be the place where you were injured. For example, if you were driving back from British Columbia to Alberta and were in an accident in British Columbia, the law of British Columbia would apply. You can hire a lawyer in either British Columbia or Alberta, but the claim itself will be filed in British Columbia and be governed by the laws of British Columbia. Some Alberta lawyers are qualified to practice in other jurisdictions (such as British Columbia), so you can certainly inquire of a local lawyer to get some guidance.
Some provinces have ‘no fault’ legislation (e.g. Saskatchewan) were it is very difficult or impossible to sue for damages for your injuries. This is why “no fault” insurance regimes are so bad.
Another situation with out-of-province injuries might result in you needing an Alberta lawyer is where the insurance coverage of the person that caused your injuries is less than the ‘value’ of your injuries. In those circumstances, you should check and see if you have an SEF 44 endorsement on your own insurance policy. If so, and your insurance is greater than the insurance of the person that caused your injuries, you can sue your own insurer for the excess ‘value’ that your injuries are above the wrongdoer’s insurance. This claim would be brought against your insurer in Alberta, even though your injuries occurred outside of Alberta.