Yes, you can get clubs you already own adjusted for a nominal fee… they can even change the length (in both directions) without reshafting them. Finding the right length and lie will fundamentally improve your game… Golf Galaxy did mine for $10 a club. For $50 it was worth it…
If you want to buy NEW clubs, you can get all that done, plus different shaft options at the same cost as a new set, assuming you don’t want a super premium shaft in your clubs.
That’s what a basic fitting is, more than anything, finding the right shaft, length and lie for you and putting them into whatever head you happen to want. A good basic fitting is usually included in the cost of new clubs (or you can pay for the fitting and order the clubs with your specs elsewhere), but that’s not always the case.
If you have a local golf store near you, I highly recommend going in and just talking to them about getting fit. See what options they have, get their pricing and see if you are comfortable with the fitter. Go when they aren’t busy, and make sure they take time to answer questions and want to help you.