You are confusing adjectives with verbs here. Adjectives change form based on gender not verbs. 'necesito' is the first person conjugation (of the verb necesitar) meaning 'I need'... so incorrect here. The subject here is the baby so this is third person singular... hence: 'necesita'.
It's one of those issues requiring some practice to get right. For example, if you just want to tell your listeners that you and specifically you, are a doctor by trade--the definite article is not used: Yo soy médico. But if you want to say more like, you are a good doctor--then the indefinite article comes back: Yo soy un buen médico.
As for the sentence above, El bebé necesita un médico, the speaker wants a physician to help the baby badly enough that he or she doesn't care about which one in particular--anyone will do. In that case, un médico is used.
Unfortunately, this is one case where Spanish becomes as prickly as French with exceptions to the exceptions. Here is a link that can help you as you practice and stumble to master it: https://www.spanishdict.com/guide/using-the-indefinite-article-in-spanish
It has a link to a quiz where you can hone your skills in using, and not using, indefinite articles.
A great way to remember this is that roles in Spanish are treated similar to some religious affiliations in English. In English, you wouldn't likely say "She is a Catholic", but rather "She is Catholic". Similarly, in Spanish, speaking about someone's role drops the article. However, you would say "I'm looking for a tall Catholic" instead of "I'm looking for tall Catholic". Adding in the adjective requires the article.
In the USA--about 60 years ago--a "GP" was a physician who received his or her medical degree, then underwent a one year "rotating" internship where they would spend several months doing Internal Medicine, several more working with surgeons, and lesser amounts of time doing pediatrics and ob-gyn respectively. After that, the physician, after passing the state's license exams, hung up a shingle announcing that he or she was a full-fledged "general practitioner," able in theory to treat patients of all ages, deliver babies, and repair a hernia now and then.
Sometime in the 60's and 70's, however, the medical industrial paradigm shifted. The GP's gradually died out and were replaced by what are now known as "Family Physicians" who settled into the same ecological niche as their predecessors. The big difference was that the FP's were now products of a three year residency program comparable to the ones training internists, pediatricians, etc. They could, and did, train under pediatricians, internists, and obstetricians, while maintaining a self-image distinct from that of the other "specialties."
Today, the Family Doctors are in the practice of providing primary care, often competing with other "PCG's," internists, pediatricians, and even ob-gyns, for the same pool of patients.
Good information. Unfortunately, in todays medical climate in the U.S., Family Practitioners often act primarily as 'gate keepers', or 'referral doctors'. They treat only the very mild conditions and have rules based on government, insurance companies, and their medical group. One rule that is common is: 3 bladder infections in one year and they refer you to a specialist...other rules for other conditions. They even have rules about how to code and how long to spend with patients to fit a code. They get paid less and are not allowed to practice the art of being a diagnostician and healer. All in all I think patients suffer, but I also think it is darn hard to be a doctor in the U.S. today. I think we are down a non-Spanish rabbit hole! Thanks again for the historical info regarding G.P.'s.
No, verb endings do not change with the gender of the subject (in this case, el bebé), but with the person of the verb. In this case, this is third person (talking about somebody else or something else) and the ending for the third person singular of the verb necesitar is a, therefore the verb required is necesita (He/she/it needs). It is first person (talking about yourself) that requires the o ending: Yo necesito (I need).
The noun bebé can be either masculine or feminine. In this sentence, the baby is male, so it's "El bebé necesita un médico." You would say "La bebé necesita un médico." if it were a female baby. "El bebé necesito" doesn't make any sense since necesito is the first person singular of the verb necesitar and would be used when talking about yourself. This sentence requires the third person singular, necesita because it's talking about "the baby".
CarsonYT, bebé with an accent on the é, means baby. Beber, means to drink. He drinks, would be Él bebe...she drinks, would be Ella bebe. Notice there is NO accent mark over the e if it means to drink, bebe. There IS an accent over the e if it means baby, bebé. Agua means water. I just watched part of your YouTube video and it looks like you are about nine years old, maybe ten. I think you are doing great with your Spanish.