As noted by Warren, the source of the noise is likely to be the pedals or the bottom bracket. Given the picture you've added to your question, I would hazard the BB needs replacement, as it looks to be in a bad shape.
It is a cup-and-cone model. The ball bearing cage has fallen apart, and the balls themselves seem rough. Finding replacement ball bearings is easy, but check the surfaces on which the balls roll: the cup (screwed into the frame) and the cone (part of the axle) should be smooth, without pitting.
If no other bike shop is available, my advice would be to find the parts yourself. If I were you, I would also try and fit a cartridge BB. To find out what parts you're looking for, you will need to know which BB shell standard your frame is made to. Measure the width of the shell, and the diameter of the hole. It is likely to be a BSA shell (68-70 mm across, with a 1.37" hole), where one side cup is left-hand threaded, and the other side has a right-hand thread. Also measure the length of the axle, should be around 120 mm.
Replacements are cheap and readily available -- A bike shop asking $150 for a BB replacement is not a bike shop I would ever visit again. A high quality cartridge bottom bracket would cost maybe $20. The fix is an hour's worth of labor if you're a complete beginner, with not many tools involved (wrenches, grease, crank puller, and cassette BB installation tool).
Sheldon Brown has some information on cup-and-cone BBs with regards to dimensions: https://www.sheldonbrown.com/bbsize.html
The ParkTool service tutorial for cup-and-cone BBs is also a great reference: https://www.parktool.com/en-int/blog/repair-help/bottom-bracket-service-adjustable-cup-and-cone