Learn Farsi: در مطب هستم و حالم بد است.

In Farsi, physical and mental states are often expressed using a noun with a personal ending rather than a direct verb. hâl means condition or state, and -am is the ending meaning my. So instead of saying I feel bad, Farsi speakers literally say my condition is bad (hâl-am bad ast).

Why is the verb hastam used in the first half, but ast in the second half?

The subject changes! In the first half, the subject is I, so you use hastam (I am). In the second half, the subject isn't you anymore, it is your condition (hâl-am). Because a condition is a third-person singular noun (an 'it'), the verb must be ast (is).

Could I add man to the beginning of the sentence?

Yes, you could say man dar matab hastam, but it is entirely optional. Farsi speakers usually drop subject pronouns because the verb ending -am already makes it perfectly clear who is at the clinic.

What is the exact meaning of matab?

matab specifically refers to a doctor's private office or consulting room. If you were at a full hospital, you would use the word bimârestân instead.