At the dDentist

After working from home, I kickstarted, an old motorbike that my "suegra"mother-in-law let me borrowed me.

you could also say "that my mother-in-law lent me"

I Wwent to pick up a relative that was at the dentist.

I usually say "who" instead of "that" if I am talking about a person or (sometimes) other animal

tThe doctor needed to apply anesthesia to the patient, since my relativhim/her, since he/she is very sensitive to pain due to bad experiences with dentists in the past,; at the end, everything went smooth. So right now, I'm more aware of my dental hygiene.

because you already said "my relative," it is unnecessary to say it again in the next sentence. Instead the pronouns that match their gender would be used.

After working from home, I kickstarted, an old motorbike that my "suegra" borrowedlent me.

I Wwent to pick up a relative that was at the dentist.

tThe doctor needed to apply anesthesia to the patient, since my relative is very sensitive to pain due to bad experiences with dentists in the past, at. But in the end, everything went smooth.ly. So right now, I'm more aware of my dental hygiene.

Very good, just be aware of punctuation and capital letters. (There is always a space after . , ? ! : ; )

After working from home, I kickstarted, an old motorbike that my "suegra" borrowedlent me.

tThe doctor needed to apply anesthesia to the patient, since my relative is very sensitive to pain due to bad experiences with dentists in the past, at. In the end, everything went smooth.ly. So right now, I'm more aware of my dental hygiene.

After working from home, I kickstarted, an old motorbike that my "suegra" borrowed me.

I Wwent to pick up a relative that was at the dentist.

tThe doctor needed to apply anesthesia to the patient, since my relative is very sensitive to pain due to bad experiences with dentists in the past, atin the end, everything went smooth. So right now, I'm more aware of my dental hygiene.