You can visually check the thickness (remaining life) of brake pad and brake disc. If its too low or closer to finishing stage better get it change.
But in your case it seems brake booster or the brake caliper/piston seems culprit as brake pedal depresses more than usual to hold the brake. Next time while driving, just pump the brake pedal couple of times and then apply brake to see if it hold faster or its still same. If after pumping, brake hold faster then that means brake booster has an issue: leaking Oring, less brake fluid, or dying itself.
Better get second mechanic opinion as it seems your current mechanic knows the secret about your deep pocket and want have his share. Wheels are having no relation with your brakes at all.