Bladder infection in baby

My daughter is 10 weeks old and we took her in to the doctor today because she had a 102.5 degree fever. They did a catheter and diagnosed her with a bladder infection (they didn't say how bad, but I'm guessing it wasn't just a small one) and prescribed her with bactrim (?) until they do the full culture. I just tried giving her the first dose and she absolutely would not take it. She was gagging and spitting it out. I tried putting the syringe all the way to the back of her throat, sides of her mouth, giving it to her in a nipple, putting her pacifier or bottle in her mouth right after, everything. She got about 2% of the dose. Is there any way to get her to take it? If she doesn't take the second dose I have to take her back in tomorrow and probably have her admitted to the hospital. 😪 any advice is appreciated.