Is it normal for the hairline to look this uneven because of the swelling after hair transplant surgery?

Dear Zombert,The simple fact is that whatever was done to your head is:permanentnot going to reveal itself for 8-12 monthsSo, this is not really the time, as your treating physician should have stressed to you on more than two occasions, to worry about the final results. The final results will be apparent 8-12 months from now, as your treating physician no doubt should have told you. For now, your hairline may look a lot “straight and artificial” but that hopefully will change over the next 10 months. If it does not, then you will need to seek the opinion of a true specialist, one who has dedicated his or her life/career to the practice of hair restoration, not one who recently acquired a cheap NeoGraft or whatever machine to do the work for them. If you were a patient of a serious, dedicated practice of hair restoration surgery, you would not have to post such questions online to an audience of unknown proportions. A specialty clinic who ONLY does hair restoration surgery is indicated. 

Your hair line can look uneven if you have facial swelling.  Sometimes it doesn't.Only time will tell.

...to worry.  Yes, asymmetry is normal and by the looks of your photos there is nothing I would worry about.  When the hair starts to grow at 6 months to a year I am confident you will be happy.

At only 1 day post-op, it's quite understandable
that you're scrutinizing your grafts and expressing concern about your results.
However, the ultimate outcome of a hair transplant procedure does take a while
to develop. It's important to give your grafts time to fully settle into your
scalp. This often requires an initial shedding process. As the days and weeks
progress, your swelling will also diminish quite a bit, and you'll be better
able to visualize your results. Be patient during this time. There's a good
chance your results will be precisely what you wanted!

It is always very difficult to make a judgement from photographs.The swelling will take a few days to go down and the new hairs will take several months to start to grow. It will be even longer before you can really begin to judge the density of the transplant and compare one side to the other. For now, you will have to be patient and follow the post-procedure instructions given to you by your doctor.