I'm wondering if one can become desensitized to the drowsy side effects of Tylenol 3.

I have rheumatoid arthritis. I don't have health insurance, so I don't have access to a rheumatologist, but I go to a wellness clinic; however, my PA can't prescribe norco after Oct 1, so he's switching me to Tylenol 3. I hate the drowsy side effects (that's why I prefer vicodin or norco--they don't make me drowsy), and I'm hoping after a couple of months I'll no longer feel drowsy when I take it. Is that possible, or do I have to resign myself to being drowsy all day every day? (It's either that or be in pain, and I've been suffering chronic pain for 7 years, so being in pain really isn't an option at this point.)

OR... Is there something I can (safely!) do to combat the drowsy side effects?