My suggestion is that instead of investing in custom fitting clubs right away, you give yourself some time to learn about what you can and can't do with the clubs that you have first.

Along with this thought, I would also suggest that you consider taking some lessons from a teaching professional to help you see the right and wrong way to ensure that you grip the club properly, set up to the ball square to the target and target line, execute your swing with correct sequencing of body motion, weight transfer, and follow-through ---- and as a part of that activity, develop an effective pre-shot routing to help with repeatability.

After you have that an understanding and familiarity with the fundamentals, you will know what to look for in a good fitter because you will have some understanding of what you need, and you will be able to better appreciate what is involved in the fitting process.

Taking lessons at a course, your pro can suggest if all or parts of your bag need replacement.

Likely not necessary to replace all of your bag at one time. You may need to adjust which hybrids and/irons need adjustment. I’d suggest putter last, so you can focus on your natural swing path without being distracted on which wedges or what driver loft will help you. One step at a time.