The cheapest and professional way to find the problem is in two free steps.
Take it to a brake shop, or wherever you would have your brakes repaired, and get a free visual inspection. Nothing obvious there? Take it to where you would have suspension/steering work done.
The free inspections are not a scam; they are a major source of customers and allow the shop to accurately estimate the cost of repairs. In either case you will get a report and an estimate without being committed to having the work done there... but that may be how you want the repair done anyway.