Yes if you take the Zyrtec about an hour before you'll be okay. It just needs to be in your system long enough to start working.
The warning is there for the doctor's protection. Always wait the 20m waiting period!! This is when most reactions occur. My BIL didn't wait once and had a bad reaction after 10m. He had to be taken back to the dr.
My son is on maintenance shots and always wants me to leave as soon as he gets his shot. He is allowed to go every 2-4 weeks for shots and is allowed to leave right after if I sign him out. I say no and we wait. He had an elevated reaction last week. We usually go every 2 weeks, but had to wait 3+ for this round due to illness. His shot location hived right up. I just gave him 'the look' and he said he was glad we'd stuck around. They have calming benedryl cream that they usually apply for reactions, and had me give him more benedryl when we got home.
If you are nervous about it, then yes take someone with you the first time. This is also why my dr. requires that a dr. be in the office for the first set of shots. If you have a local (hives/itching) reaction they will give you some lotion. If you have a problem with your breathing or passing out, they have other medicines that they can use asap.