NEED to buy an A1175 Battery

Not knowing the EXACT model/year MBP that you have, there are two battery choices available that have been determined to work well in MBPs by veteran ASC participants. Look for ANKER and NUPOWER:

https://eshop.macsales.com/search/macbook%20pro%20battery

Both can be user installed (unless you have a retina MBP).

Apple will not sell you a battery directly. If you have a newer MBP, then they will insist on installing for you.

Ciao.

Sounds like yo have among the earliest MacBook Pros. The A1175 battery only works in the old "silver keyboard" MBPs (2006 through roughly 2008) that Apple considers obsolete so, as you have found, they no longer sell the battery either. Officially, Apple or AppleCare does not have to look at anything that old. A kindly tech in one store may at least give you some suggestions but their "official" policy on products deemed obsolete are spelled out pretty clearly in this Apple article:

Vintage and obsolete products - Apple Support

I add my vote for the NUPOWER models from Other World Computing. OWC has excellent customer service should the new battery prove unsatisfactory.

Understand that a swelling battery may have already damaged other components in the computer; the trackpad and keyboard are most vulnerable. If you can find an independent Apple repair ship, they may be able to tell if anything else is damaged before you lay down the money for a new battery. If you need a new battery plus a keyboard and/or trackpad, repair on such and old MBP is probably not worth expense.

You may also want to peruse iFixIt's pages for details on how to get the bad battery out and parts: https://www.ifixit.com/Device/MacBook_Pro

Call Apple Care. Tell them your battery has expanded. If your Mac is still under warranty, then it won't cost. If not under warranty, it will cost. Either way, you have to return the bad battery in the mailer they send with the new battery.

Have a nice day.

Boyd