No credit card required
Browse credit cards from a variety of issuers to see if there's a better card for you.
You will get that cards instant history so your AAoA will go way up. Your overall CL will go way up but since you keep a small balance it won't really help there.
Personally, even if you obtain a score boost, I would think twice about adding history of another to your credit report.
It is not all about your three-digit score.
By adding the history of another to your report, and thus scoring, it makes your score no longer a measure of your own, personal repayment risk.
If a creditor chooses to do a manual review of your CR, which is likely should you apply for higher credit limits or higher principal credit, they will immediately see that your score was calculated based on history of another. If they wish to see your score based only on your own history, which is what a FICO score is supposed to measure, they simply cannot do that. They cant back out items and run their own score. It thus could make your enfire score questionable for their evaluation purposes.
Having history of another as part o your scoring is beneficial primarily where creditors rely primarily or only on your score, and dont do a manual review. That is done as a cost saving measure where the credit sought is low, and thus of lower risk. Great for those rebuilding.
With your history and score, you are not in a rebuilding mode, so addition of an AU could raise unecessary issues upon a manual review.