It's normal, but frustrating.
There are a couple of ways to deal with this. One is to invite the sitter over and just have her stay in the room with you. Graduate to having the sitter hold your baby but facing out (toward you) while you entertain the baby - make funny faces, sing, use puppets, anything. Then walk around with the baby, with the sitter holding her, while you point at things out the window. Go outside with the stroller (weather permitting - ha ha, not so likely in Philadelphia right now) but you can go to the mall and get your baby used to seeing other sights and being distracted while hearing the sitter's voice. Then you veer off for a while and have the sitter keep going with the baby. Meet up after 5-10 minutes and have the sitter put the stroller toward you and "voilá - there's Mommy!" Then do it a few times where you walk away for a minute, then 5, then 10 - eventually the baby gets the idea that Mommy comes back.
The other way to do it is to let her cry - usually they don't scream for that long, and a professional sitter or day care person understands how to cope with this.
When you say you haven't been out because no one wants to deal with the crying, what do you mean? Have you tried it and you can't get those sitters to come back? Or have you been using relatives who don't have the patience or a sense of detachment where they can hear a baby cry and not take it personally? The key is to distract the baby, not to talk her out of missing her Mom. And are you not going out with the baby to expose her to other sights and sounds? Is it possible that your baby is used to the quiet of the home and is reacting to the stimulation of other settings and not specifically to your absence? That's another issue entirely. Start slowly - but get out of the house! You can go to a mall early, before the stores open when the mall itself is open for walkers and joggers - it's not super noisy or crowded, but there are people, sometimes some background music and maybe a fountain you can take her too. Otherwise just look in the windows - colors and shapes are important for a child to take in. It's essential that she get used to a stroller - and pretty soon she'll figure out that it doesn't much matter who's pushing the stroller when she can't see the caretaker anyway!
I was 37 when I had my son, and he was like this for a while. Sometimes when we're in our 30s, we think we're supposed to know more about this mothering stuff, but it's still brand new! And every kid is different, and goes through phases. I hired a mother's helper (a neighborhood kid) while I stayed home and did laundry or paid bills, just to get him used to me not being in the room all the time. Then I ventured out. If he cried, I couldn't hear him. But I had been out with him from the beginning so he got used to other sights/sounds.