No, 22 months is not too young for a babysitter.
No, being concerned about getting one is not weird. Especially when you can't use family or someone you already know.
First kid, first sitter, it can be a big deal for parents. I was reluctant, too. Of course now days I'm waiting on the front porch for her, and yell "food's in the fridge" as I zoom past her in the driveway.
Find one you BOTH like. Meet with them first with no plans to actually take care of your son. It's impossible to really be comfortable with the idea of a sitter until you find someone, see a face, and talk to them a little bit.
Then have him/her watch the kid while you're both there the first time, if the house is big enough to not all be piled in the same room (do something in the other room, don't hover).
Next time leave the house for an hour. More if you're comfortable. But an hour is good if you're not entirely ready yet.
It's totally normal to have some reservations and anxiety about getting a sitter. That's the most important thing in the world he/she will be taking care of. But easing into it will help. And if your son isn't used to strangers, easing into it will be good for him, too.