As a rather sweaty guy myself (I do suffer from hyperhydrosis and also am a bit of a fat fellow) I can completely relate to the OP (yes, I realize that the original post was in 9/2016). A couple tips to help those who suffer from these problems:
1.Get your doc to prescribe a prescription antiperspirant. Yes, there are Rx ones that are much better at stopping the sweat than the regular ones.
2. Carry an extra pair of undergarments with you. Not just a regular uniform, but the entire undergarment set you wear. Even if you don't think you need to, change 1/2 way through your shift.
3. Medicated body powder. Not baby powder. The medicated stuff absorbs better and is altogether a better thing.
4. Fabric Softener. This really helps pull the odors from the clothes and replaces them with a nice fragrance.
5. Lots and Lots and Lots of Water.
6. Some more water.
7. Shave your pits and do some landscaping south of the belly button. Less hair means less places to catch the sweat and to build problems. This is especially important if you suffer from bromhidrosis like I do, which is a disorder of the apocrine glands resulting in a very foul body odor.
8. If you have a station, shower at least once a shift. If not, see if your area has a truck stop/gym. If you are having a problem with smelling on shift, most if not all agencies would allow you to make a shower happen. I used to work for a large private EMS service that was system status, and about halfway through shift, my supervisors knew I was out of service for about 10-11 minutes while I showered at a local gym. I had discussed my issues prior to employment with the agency, and they were absolutely understanding of this. At my current employment, if I need to go out of service to take a shower, I simply call my shift captain and do so. It is much easier now that I work for a service that has stations though.
If anyone has any questions, feel free to hit me up.