Try not to worry, it can be daunting at first. Especially if you don't have family nearby and don't drive (I don't).
It took me till dd was about 5 months old before I left the house with her alone. Other mums seemed to find it so easy but dd wouldn't nap during the day, hated the pram and would cry frequently.
Try short trips out at first, between naps, to shops or playgroups or childrens centres. Places you can always leave as and when you need to.
Do try to get out, it'll be good for both you and the baby. A 10 mth old can get a lot out of a bit of singing, change of scene, different toys, seeing other children etc. And other mums are usually friendly and sympathetic. Don't isolate yourself unless you genuinely believe that's best for you both.
We've never left our dd (now 2.6) overnight and only started using a sitter very recently (though have used nursery since dd was 1). We worried about nursery but its been the making of dd. Her sleep improved massively and she is thriving there.
I'd recommend finding one or two local sitters you trust (if family can't help) now rather than later, so they can get to know your baby. We use an agency who have local, older, very experienced sitters who are mostly ex or current nannies/CMs. PM me if you want any more info.
The sitter we use is fab and although I was really worried about using one, I now wish we'd started using one ages ago. You need some time as a couple too.