There are a couple of things you can try. They always work for me and you buy them at Home Depot or Lowes.
I got an industrial very strong drain cleaner called "Instant Power" Creates heat to dissolve hair and grease contains concentrated lye. The 33.8 oz black bottle with red and yellow lettering comes with a plastic bag around it. (Description so you can recognize it)
You can't get this in a grocery store, only a hardware store. I got it at Home Depot There are probably other similar products but I know this one works. I would try this first!
The other thing I use is a drain bladder. They have different sizes for inside drains or the main cleanout outside. I have used the 4" main bladder many times.
The way it works is you connect it to your garden hose and feed it into the drain as far as you can. Then you turn on the water and the bladder expands to close off the drain. It starts shooting water and blasts everything away that's clogging the line. This thing is the greateat!
At the main, the line goes toward the house and away from the house toward the sewer or septic. I have even shot the water towards the house to break up a clog that has not reached the main cleanout, but watch and cover the drains in case the clog breaks loose.
This drain bladder is really easy. Just put it on the hose, shove it in the drain and turn the water on.
The only problem I have found with the small inside bladder is getting it into the drain. The sink and tub drains are always blocked by some kind of fixture like a stopper or the drain cover thing in the kitchen sink...haha... I don't know what it's called but you know...
I'm certain one or both of these things will work. It way cheaper than a plumber and nobody has to see your house.
Good luck, Beverly