Hello Rianne80,
I will try and shed some light on your problem. If you have a forward head posture you will need to draw your head backwards and tuck your chin under gently.If the muscles on either side of your neck are tense then you will feel the stretch. This is not the same as moving your head backwards into extension.This often causes dizziness especially when women try and hang washing up on the line. It closes down the facets joints when you do this.If you tuck your chin under then the muscles around the larynx shouldn't be on a stretch.Because your head is tilted backwards you are getting the mucus running down.You need to do this deep neck flexion exercise especially if you have hypermobility.
Are you short in stature as if this is the case you will be constantly looking upwards, so remember to tuck your chin in gently.

One of the possible reasons for your voice sounding strange could be acid reflux as this is especially noticeable after eating.The acid runs up and irritates the vocal chords causing hoarseness. This would also explain the coughing as it could be the acid reflux or the post nasal drip. You may need to exclude any hayfever/allergy etc if this is recurrent.
Tension at the best of times doesn't help and you will be holding your jaw tense too, may be.

If you want to know more about how to look after your neck I have a neck book called "Don't let neck pain ruin your life" on Amazon Kindle selling for £2.98.
Don't feel pressured to buy it but I feel for you as neck pain is horrible.
Hope this helps,
Regards,
cam474