The shower valve is very hard to pull out. I do not have a brand or model at this time. It is a single valve that you pull out and then adjust hot/cold water by turning valve left and right.
I am new to this site; why does it say it was posted at 6:37pm when it is 11:37am in CA

If you have an acrylic handle with a teardrop design, you have a moen château. Call moen customer service and you may fall into their 'lifetime' warranty. You need a moen 1225 b cartridge. If you do this job yourself DO NOT TURN THE CARTRIDGE MORE THAN 11:00 TO THE LEFT OR 1:00 TO THE RIGHT AND DO NOT BREAK THE HORSESHOE CLIP. If you buy the replacement cartridge, get genuine moen. Danko is a clone and sometimes do not work well.
Kissler & Co., Inc. : For all of Your Plumbing Repair Parts Needs
Find your handle here.

All times are GMT times so in the PDST you are 7 hours behind GMT that will change to 8 hours in October when the time changes. I think I am correct unless I am just backwards. After all I am just a plumber.

This happens when the "O" rings swell up and bind the cartridge.

To change a Moen Cartridge you must first, Remove cap (kitchen) or insert button (bathroom) to expose screw.
Remove the screw and pull off handle assembly.
Turn off shut off valves to the shower valve.
Remove retainer clip (copper horseshoe shaped clip) and pull out cartridge with channel locks, pliers, or cartridge puller. Lube new cartridge with silicone jel and
Insert the cartridge with hole on the stem facing the 6 o'clock position, or down in a tub/shower.
Reinsert retainer clip and screw in handle assembly, followed by the cap or insert button. Turn water back on under sink. My company uses Moen valves on all their new construction. Moen makes a "cartridge puller",(see image) That will get those stubborn cartridges out of the valve body if you have a problem. Good luck, Tom

I have taken it apart and it looks like it is a Price Pfister. I cleaned it and then put the cartridge on the counter and my wife decided to help and put baby oil on it. It seems to work fine now but what is the baby oil going to do to the rubber seals

What is the baby oil going to do to the rubber seals?

In time any petroleum product will cause the neoprene to get "mushy" and deteriorate. But it will take a while and then you can replace the cartridge.
Regards, Tom

Price pfister has a lifetime warranty. Call 1-800-pfaucet and tell them you are having problems. Do not tell them you put baby oil on it. They will send you a new cartridge free.