Trying to get to know her is not bad unless she doesn't want contact. It can actually make things easier. Being jealous is not crazy. It's an indicator that something is "off" about the situation. Maybe you are afraid or insecure. Is your relationship with hubby strong? Are your needs currently being met? If not, what needs to change? Are you worried he might like her better or leave you? That you will not have as much time with him or less sex? Any number of other concerns can play into it. You are not doing it wrong just because you have feelings. Those are natural.
Try to track them down, though. Visualize different scenarios, dates, sex, pillow talk, etc. To help you figure out which things bother you and which don't. Then you can start making a plan on how to deal with the triggers or identify problems that need to be corrected to help everyone be happy. You should probably also let your husband know you are dealing with jealousy but assure him you are working on it. Take things slow and give yourself time. Most o f all, give yourself a break. If you're not engaging in psychotic behavior, jealousy does not mean you're crazy or doing anything wrong. It just means you have room to grow or have picked up on a problem you haven't consciously faced yet.