It's been about 8 months since your range was limited by illness. You mention slowly re-building your range: How long did this process last?
This article by an otolaryngologist explains:
Fortunately, the common cold and the flu are self-limiting infections, which resolve in 7 to 10 days. For the singer and vocal performer, full recovery may take 2 to 3 weeks, which seems like an eternity when singing is your raison d'etre.
As such, expert advice would suggest that your range should've returned months ago if it were limited by a cold, so we need to expand our differential diagnosis:
You also mention "I can sing pretty low, down to an E3 with proper warm up" (were you able to sing this low before last Christmas, when your upper register was intact?) and that you are a twelve-year-old female. This combination leads me to believe that you're going through puberty-driven physical and hormonal changes. As you grow, your lungs will enlarge and your larynx will lengthen, and increasing androgen levels in adult men and women correspond to a decrease in vocal fundamental frequency. Fortunately, you have relevant academic research at your disposal:
"The Adolescent Female
Changing Voice: A
Investigation" (Journal of Research in Music Education, Sweet, 2015) is a phenomenological study, meaning that it focuses on the experience of being an adolescent female with a changing voice. It may be useful for you to read about the experiences of other young females who went through this process in a choral setting.
The essence of the experience of female voice change was
that vulnerability and fear of embarrassment determined all use of the females’ singing
voices, resulting in risk assessment for each singing situation and setting.
Knowing this, you'll be better-prepared emotionally for the hardships and frustrations that come with being a musician whose instrument is not entirely in your control.
"Physiological Changes in the Adolescent Female Voice:
Applications for Choral Instruction" (honors thesis, Haston, 2007) delves into anatomical changes and even includes vocal exercises to maintain and expand your range.
The time in which physiological
changes occur during vocal development is
one of the most fragile points in a young woman’s life. If her vocal instrument is misguided and/or mislabeled due to ignorance on the part of the teacher, a talent could be lost, wasted,
damaged, or at the very least its potential will only be partially realized. Each
educator must take the time to educate him/herself in the current research
available on the changing female adolescent voice. A music teacher must not
only teach notes and rhythms, but also instruct his/her students in vocal
technique and health in order to ensure
these students have their own unique,
This echoes the best advice I can give you: Find a great teacher. They will guide you through illness, puberty, difficult repertoire, and whatever other musical or personal challenges you bring them. For the time being, you can work on your range with normal exercises, but don't push yourself to the point of discomfort. Right now, your anatomy might be limiting you to an E5 and forcing your voice higher could do damage. Until you find someone who can offer you professional guidance, treat singing like weightlifting: Don't go for the extremes of your range until you're warmed-up and have expert supervision.