Listen to your doctor and go to the hospital. Infections from tooth decay and sinus infections can go south pretty quickly if they aren't addressed appropriately. Doctors will treat people outside of the hospital whenever possible, if they are telling you to go to the hospital, you should listen. If your body could fight this infection without help, it would have knocked it out already.

If it helps, you can go with your girlfriend. She can help with talking to the doctor, help manage discomfort, or ask the questions you forget about if you're not feeling well. This is a thing that people do all the time for family members that don't speak the language. Totally legitimate for you to invite them in.

If you choose to go to the hospital to be seen make sure and tell your nurse and doctor about your reactions to previous antibiotics. There are plenty of others they can prescribe.

If you have to stay overnight communicate your feelings about that to those taking care of you. They can’t help you if you don’t let them know how you are feeling.

If there is something reasonable they be an do to help accommodate you they will. Need less interactions? They can put a do not disturb sign on your door and just check in on your minimally. Ask all the questions you have about anything that makes you anxious.

I'm not a doctor, but when my dog had a tooth infection the vet was pretty concerned. Teeth are close to the brain and eyes and if an infection spreads it's bad.

And the hospital doesn't want to keep you overnight, either. If they insist there will be a good reason.

Well infections are pretty serious so going to the hospital seems to be a must. Make a note of the medicines you've had bad reactions to and mention them to the doctor/nurse there. I know hospitals are scary, I hate them too. If you have anyone you can go with, ask them. If not, take something to give you comfort, you'll be waiting a lot there. Unless it's ridiculously serious, I doubt they'll hold you overnight. Likely they'll assess the infections the best they can, prescribe some antibiotics, and tell you to follow up with your primary doctor. Besides the emergency room, "urgent care" is also an option, but your mileage may vary how good they are. They're like emergency room, but for less severe stuff and focus on quickly assessing you, rather than a more thorough triage that a hospital might give. Again, be sure to mention your reactions to the medicines you were given. I hope you can get the help you need.