36 Weeks Pregnant With Twins: Outside Stress, Getting Sick When You're Pregnant

I am 36-and-a-half weeks pregnant with twin boys and am chugging along towards a C-section finish line -- well, not without bumps in the road.
This week has been particularly difficult. No, not because of the fatigue, kankles or restless legs -- although these issues aren't helping. My dad was admitted to ICU at his local hospital Sunday for acute respiratory distress syndrome (ARDS), which was causing his kidneys to shut down -- they were giving us a 50/50 chance he'd recover. After four days in ICU, he was moved to a regular hospital room, thankfully, but needless to say it's been stressful and he still has rehab ahead of him.
On top of this, I developed a cold. Well, at least I think it's a cold -- headache, sore throat, gunky. When I woke up with these symptoms yesterday, I also woke up with a stiff neck from sleeping on it wrong. Ouch.
All in all, I was concerned about how stress affects my pregnancy. Can the babies feel stress? Will it make them stressed? Will I go into labor early from stress? I spoke with my doctor about these concerns at my latest appointment and realized a pregnancy without stress is nearly impossible. With that in mind, some doctors say it may even be good for babies (I'm talking a normal amount of stress, not some extremely stressful, freak event) because life is not without stress and it may prepare them better for when they make their grand exit from my body. All I can do is breathe, try to relax and even try to talk it out with my babies, which will help me connect with them and also get through my stress.
I.e. saying out loud, "I am feeling sad because my dad is sick but thankfully he is getting better."
With my cold, I'm gargling salt water, eating healthy, resting, sleeping even more, drinking some orange juice but also drinking plenty of water. I'm trying to keep away from medicine even though I understand it is safe to take Tylenol.
Honestly it's hard to know what I'm feeling because of the cold and pregnancy hormones, so I'm just going to try my best and keep chugging along.