I have been feeling better is a statement about your present state; the present perfect construction indicates that that state started in the past. The since clause designates the start of that state, the point in time at which it began. In this case it began with an event, the doctor's coming, which was completed in the past.
- That cannot be expressed with a), the present perfect, the doctor has come, because that, again, designates a present state.
- It cannot be expressed with b), the future, the doctor will come, because that designates an event which has not happened yet.
- It cannot be expressed with c), the past perfect, the doctor had come, because that designates a past state which came after the doctor's coming.
It is properly expressed with the simple past form, answer d):
I have been feeling better since the doctor came.
On a sweltering day, the intended meaning should be picked up on easily enough. But your father might be helping you out by pointing out a potential double-entendre – sometimes those can be embarrassing if said around the wrong group of people. For example, if a teenage girl is surrounded by teenage boys, "I feel hot" might not be the best way to word her feelings about the hot day. (Even if they know what she means, they might start snickering anyway.)
You ask for an alternative, so I'll give you one:
This heat is killing me.
That's a bit figurative, too, so you could also say:
This heat is really getting to me.
Here's another one:
I'm not enjoying this hot weather.
Most of the time, though, "I'm feeling hot" is just fine by itself, and there's no need to find a more ‘sterile’ alternative. Most people know what you mean when you're talking about the heat in a room, or the heat outside on a sweltering day. I'm not recommending that the phrase be avoided altogether, but it's worth remembering that it can be interpreted in more than one way.
NOTE: Some earlier comments seemed to be skeptical about this double meaning, so I'll back my assertion up with a few examples. When these bloggers write:
Pick a dress that compliments your figure. If you’re wearing red, you want to look and feel hot!
If you feel hot, then you’ll look hot. Confidence is your greatest accessory.
The point is that you will be dressing to impress him somehow, while you make yourself feel hot and confident.
they are not meaning that you'll need to sit near a fan and sip a cold drink to cool off. Moreover, these authors were dishing out some fashion advice for Valentine's Day (which is celebrated in February), so we can be pretty sure that weren't talking about hot weather, either.
That said, even in fashion circles, the phrase can be used both ways. There's a big difference between hot & confident and hot & itchy. Check out these excerpts:
Don't wear anything that’s going to make you feel hot. Sweaty is not sexy.
The long sleeves will help keep the direct sun off of your arms but without making you feel hot and sticky.
In those sentences, follow-on remarks make it clear that "feel hot" in that context wasn't intended to mean "feel sexy."
Best Answer
Or you could make the sentence shorter because the "to him" is implied: