For some background on the plant, it's an indoor plant and we've had it for approximately 10 years (give or take 3 years). Just last year we had a slight problem with these tiny spiders that were spinning webs around the plant but it was quickly resolved when someone recommended spraying soapy water on the leaves.

For the past few months our plant has got these weird little bumps that resemble a type of pest but they don't move and just cling to the stems and bottoms of leaves. The unnecessary stress brought upon the plant causes it to secrete sap which gets all over our floors and is a giant mess to clean.

I have already tried wiping off each individual leaf with soapy water and another time with rubbing alcohol diluted in water (yes, what a good daughter I am... I clean the plant better than I clean myself)

If anyone has ANY idea what this possibly could be, please let me know. Even if you don't know what it is please give me any suggestion that could possibly cure our plant

That is scale. You did good by using alcohol/water mixture, but that is not enough.
Even if you clean what 'bumps' are visible, there are probably more left in hiding places.
I only had mild scale problem so far & alcohol was enough, but you may have to do more. You can search this forum for lots of good suggestions - here I copied something for you, posted by Al (tapla) in another thread:

Posted by tapla z5b-6a mid-MI (My Page) on Mon, Aug 27, 12 at 4:03

Imidicloprid is an over-the-counter insecticide that is effective against scale. It is available in a vehicle designed to be sprinkled on the soil, a liquid soil drench that usually has no mixing directions for indoor applications, and in preparations designed to be used as a spray, but the actual spraying needs to be done outdoors and the application allowed to dry on the plant before bringing the plant indoors. I find the later (the spray) to be most effective for houseplants, particularly for trees and other plants with woody stems. I use Bayer Advanced 3-In-1 Insect, Disease & Mite Control, which is an excellent product when scale infestations occur, and can be used against mites. The product also includes a systemic fungicide that is very effective as a prophylactic and a fixitive against most fungal infections, should you encounter one. All in all, it's a good multiple purpose product to have at your disposal for indoor or outdoor containerized plants, but remember to follow directions and particularly that the spraying is to be undertaken outdoors only.
Also effective against scale are horticultural oils that have the word(s) light - summer - or all-season in their names. When using the oils, COMPLETE coverage is required or it's likely the infestation will be recurrent. Neem oil is also very effective against scale, but requires persistence. Often, being faithful to 4-6 applications at 2-3 week intervals are required to rid the plant of reproducing adults. Home remedies like alcohol preparations and fish emulsion solutions may have some knockdown effect on predators in the crawler stage, but leave adults under their protective shells largely unaffected, leaving eradication by these methods unlikely.

Al

Al, I hope you don't mind...Thanx.

Here is thread above is copied from (for more ideas how to deal with scale):
click here to read more

(Make sure you don't leave plant in sun when you apply any solution, it will burn the leaves more than likely.)

Rina

Adult scale insect latch onto a promising location, insert their little needle-like beaks into the plant...and siphon plant sap from that one spot for the duration of their lives. That sticky sap is called 'honey dew'...it's the excrement from the scale insects.

Planto

Al

Your plant looks like a Night Blooming Cereus! If this were my plant, I would cut the plant back drastically until no sign of scale was visible. I would then spray it with a solution of warm water, Neem Oil and Dawn Dish Detergent twice a week for about 6 weeks. Once it produces new growth repot it and spray again for about 3 weeks. That should take care of the scale. Good luck!

correct me if I am wrong, but isn't Night Blooming Cereus a cactus? This plant doesn't look like cactus to me...?

You might not like the fishy odor, but Fish Emulsion killed every single scale on an Olive tree shipped from a nursery.

I didn't notice scale at first, so it was placed between two citrus trees. A day or two later, while misting, I discovered a vast amount of brown bumps on my new plant. Both citrus branches nearest the olive were covered with these awful insects.

A grower in Florida where my citrus were purchased told me they use Fish Emulsion as a scale preventative. I followed her directions, sprayed my plants with Fish Emulsion and water.
The scale-infested tree was shipped here 1999...to this day, 'since I spray w/FE twice a year,' my plants have been scale-free.

Fish Emulsion has a fishy smell, but works and is organic. It's also used as an organic fertilizer...the odor is harmless to humans and pets. And it works.

Do you have a picture of your entire plant? Toni

Planto

Yes, FE works great. My olive tree was so infested, same with the citrus branches, yet after spraying with FE, every, single scale died.

Before bringing plants indoors in autumn, each plant gets a good spraying with FE and other home made ingredients. Toni

Planto

Glad you're well. Actually, I was very ill beginning in July, got worse in August. Feeling better now.

Ingredients. For Scale, FE alone does the job, but preventing/ridding other insects such as Mites, I mix a bunch of home-made ingredients together.

Water
2-4 drops dish soap...'not liquid Dawn.'
Garlic
Hot Pepper
Citrus peel or juice
Listerine, 'mouthwash.'

If absolutely necessary, cigarette butts..I do not recommend cigs, but it's a sure way to kill unwanted insects. Cig butts is the only ingredient that can be harmful to a plant. I prefer organic...refuse chemicals.

Now, if I can find a way to rid Mealy! lol.

For years, my plants have been insect free. I spray w/above ingredients every other week, minus cig butts and FE.

Before hauling plants indoors before winter, each plant is sprayed w/this concoction plus FE. Because FE works as an organic fertilizer, I consider FE to work as a last feeding before winter.
BTW, when plants are sprayed every other week, all but FE and cigs is included. I only use FE in spring and autumn, unless a newly shipped plant happens to be scale infested.

Works for my plants w/o nasty chemicals. Toni