Things like that happen sometimes. Have a big heart and forgive. Give her the gift. Allah swt will give you better friends inshallah, if you forgive. Be a better person, for yourself. Maybe at another time you may want to mention how hurt you were when she didn't invite you at her birthday. However don't mention it while you are giving the gift. Mention it like a month later if its really bothering you still,"Maria, somethings just been bothering, remember that one day on your birthday..." If she says sorry, just forgive or let go.
Consider this whole scenario an oppurtunity to be a better person. It's your chance! Don't lose it!
Ditto