Not ure what the other repsonses are, but thought I'd throuw my 2 cents in.
Yes, you can spoil a baby, but that is subjective. IMO, babies need to learn how to self-soothe, and they will at some point. Some take a longer time than others, and it depends on how much you are willing to deal with.
Three months though, is still pretty young, so I wouldn't worry too much. If you can, use a sling or something similar that lets you be hands free (or at least on hand free!) and go about your day. Try to give her more "away from mommy time" as you can, and she'll be ok.
Spoiling is subjective...if it doesn't bother you, don't let what other people say bother you.