Hello, so today I was riding and as I pedaled there was this off and on feeling/sound of something grinding under the cassettes or on some moving part on the bike. I just called a local bike shop to see if I could get my bike deep cleaned which they told me would cost 85$ (that's insanely expensive), so I decided to do it myself, however I have zero bike tools with the exception of a hex/allen wrench. Is it still possible to clean everything?

If you really want to clean EVERYTHING, you'd pretty much need to disassemble everything as well. And that requires a handful of special tools and associated knowledge.
Why not start simpler?
A bucket, a brush, some rags, water, detergent and some lube is all it takes to give the drivetrain a good wash. I suggest you start there.

Depends on your definition of "everything".

If you're getting a grinding sensation when pedalling, it sounds like the drivetrain could be dirty. Cleaning the chain really well generally requires either one of those on-the-bike cleaning machines or removing the chain, which may or may not require a tool, although you can usually get the rear sprockets and the chainrings fairly clean without taking off more than the rear wheel.

I mean everything as in the chain (which I cleaned yesterday), the cassette, and in between the pedal cranks

Is it okay to spray your chain/cassettes with a hose or would that cause rusting?

85 dollars sounds pretty good
considering they probably have to remove the whole drive train
then clean it
then put it all back together
and adjust it to function like new

maybe it is not insanely expensive
but you are insanely cheap

No, that is not OK for mine, but it probably is for yours.

Googled some shop rates for drivetrain cleaning. Most show rates of $30-40. You might inquire for the shop's rate for this service, rather than deep cleaning.

To do this yourself doesn't require expensive tools. You can do a decent job on the rings and cogs with a brush. A chainwhip and lockring tool are handy for cleaning the cassette off the wheel. Some cranksets require little more than a hex wrench to remove, if you wish to go that far. Chainrings and derailleur pulleys also come off with a hex wrench.

If this is the only bicycle you will ever own... and the only time you might need to do simple repairs... then you don't need tools.

Let on line shopping be your friend. Amazon.com, performancebike.com, and nashbar.com all have inexpensive bicycle tools and tool kits. Your local library will have bicycle repair manuals (also available on line). And tons of great bicycle repair maintenance videos on Youtube.

I am big believer that if you can't fix it... you don't own it. You're only renting it from the repairman.

If you can't clean your own bike and $85 is insanely expensive for whatever a "deep" cleaning is, I would suggest that you cut your losses now and start looking for running shoes.

But.........eighty-five bucks won't buy much more in shoes than it will in bikes.

I'm at a loss for suggestions.

Dang no need to get offensive, unlike most of you on here I'm still a new to cycling and I don't know what is a good price for cleaning. 85$ is a lot to me considering all other cleanings at the shop are about 10$

I'm looking at all this bike cleaning videos on Youtube and in all the video's they're spraying down their bike with a hose

Just proves the people making the videos don't know what they are doing.
Water inside the freewheel or cassette is bad. Water inside the bottom bracket ( either sealed or loose bearings) is bad. Water and grease do NOT mix. Water causes rust. Rust causes pawl springs to break. Water causes grease to cake/become hard. This causes cassette/freewheel pawls to skip - or worse to happen inside.
If you hose bike, don't use high pressure; just what ever flows out the open end. When finished, spray the hell out of the inside of the freewheel/cassette with WD-40 or equivalent. Dry and lube the chain.

Is there a Bike Co-Op in your area? You may be able to go there to do the work, using their tools and expertise if you run into problems or have questions.

Thank you, I rinsed my cassette and chain with water and I'm about to dry it then lube the chain and spray the cassette with WD-40. For the first time after many failed attempts my chain is actually clean, it seems like the store bought White Lightening Degreaser doesn't work well.